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## Heath-Brown, Roger

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 Author ID: heath-brown.roger Published as: Heath-Brown, D. R.; Heath-Brown, Roger; Heath-Brown, David Rodney; Heath-Brown, D. Roger; Heath-Brown, D. Homepage: https://www.maths.ox.ac.uk/people/roger.heath-brown External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef
 Documents Indexed: 188 Publications since 1974, including 4 Books Reviewing Activity: 709 Reviews Biographic References: 1 Publication
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#### Co-Authors

 130 single-authored 16 Browning, Timothy Daniel 6 Moroz, Boris Zelikovich Baruch ben Zelik 4 Pierce, Lillian B. 3 Iwaniec, Henryk 2 Banks, William D. 2 Bui, Hung Manh 2 Conrey, John Brian 2 Dietmann, Rainer 2 Goldston, Daniel Alan 2 Jia, Chaohua 2 Konyagin, Sergeĭ Vladimirovich 2 Li, Xiannan 2 Manin, Yuri Ivanovich 2 Shparlinski, Igor E. 1 Adleman, Leonard Max 1 Balasubramanian, Ramachandran 1 Dieulefait, Luis Victor 1 Evelyn, Cecil John Alvin 1 Faltings, Gerd 1 Ford, Kevin B. 1 Friedlander, John Benjamin 1 Gallardo, Luis Henri 1 Garaev, Moubariz Z. 1 Ghosh, Amit 1 Gonek, Steven M. 1 Halberstam, Heini 1 Huxley, Martin N. 1 Kaczorowski, Jerzy 1 Lioen, Walter M. 1 Macintyre, Angus John 1 Matiyasevich, Yuriĭ Vladimirovich 1 Michel, Philippe Gabriel 1 Micheli, Giacomo 1 Patterson, Samuel James 1 Praeger, Cheryl Elisabeth 1 Richert, Hans-Egon 1 Salberger, Per 1 Schlage-Puchta, Jan-Christoph 1 Shalev, Aner 1 Skorobogatov, Alexei Nikolaïevitch 1 Starr, Jason Michael 1 te Riele, Herman 1 Testa, Damiano 1 Tolev, Doychin I. 1 Tsang, Kai-Man 1 Wilson, Pelham Mark Hedley 1 Wintenberger, Jean-Pierre
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#### Serials

 14 Acta Arithmetica 12 Journal of the London Mathematical Society. Second Series 12 Proceedings of the London Mathematical Society. Third Series 11 Journal für die Reine und Angewandte Mathematik 8 Inventiones Mathematicae 8 Mathematika 7 Bulletin of the London Mathematical Society 6 Mathematical Proceedings of the Cambridge Philosophical Society 6 The Quarterly Journal of Mathematics. Oxford Second Series 5 Journal of Number Theory 4 Duke Mathematical Journal 3 Mathematische Annalen 3 Mathematische Zeitschrift 2 Israel Journal of Mathematics 2 Mathematics of Computation 2 Acta Mathematica 2 Canadian Journal of Mathematics 2 Compositio Mathematica 2 Functiones et Approximatio. Commentarii Mathematici 2 The Journal of the Indian Mathematical Society. New Series 2 Revista Matemática Iberoamericana 2 Forum Mathematicum 2 Journal of Mathematical Sciences (New York) 2 The Quarterly Journal of Mathematics 2 Journal of the Institute of Mathematics of Jussieu 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Russian Mathematical Surveys 1 The Mathematical Intelligencer 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Helvetici 1 Glasgow Mathematical Journal 1 Hardy-Ramanujan Journal 1 Analysis 1 Science in China. Series A 1 IMRN. International Mathematics Research Notices 1 Geometric and Functional Analysis. GAFA 1 Bulletin of the American Mathematical Society. New Series 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Finite Fields and their Applications 1 The Asian Journal of Mathematics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 International Journal of Number Theory 1 Bonner Mathematische Schriften 1 Lecture Notes in Mathematics 1 London Mathematical Society Lecture Note Series 1 Proceedings of the Steklov Institute of Mathematics 1 Science China. Mathematics 1 Discrete Analysis
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#### Fields

 186 Number theory (11-XX) 29 Algebraic geometry (14-XX) 4 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 2 Group theory and generalizations (20-XX) 1 Dynamical systems and ergodic theory (37-XX)

#### Citations contained in zbMATH Open

160 Publications have been cited 1,993 times in 1,509 Documents Cited by Year
Artin’s conjecture for primitive roots. Zbl 0586.10025
Heath-Brown, D. R.
1986
The fourth power moment of the Riemann zeta function. Zbl 0403.10018
Heath-Brown, D. R.
1979
The Pjateckii-Sapiro prime number theorem. Zbl 0513.10042
Heath-Brown, D. R.
1983
The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène). Zbl 1039.11044
Heath-Brown, D. R.
2002
Zero-free regions for Dirichlet $$L$$-functions and the least prime in an arithmetic progression. Zbl 0739.11033
Heath-Brown, D. R.
1992
Prime numbers in short intervals and a generalized Vaughan identity. Zbl 0478.10024
Heath-Brown, D. R.
1982
New bounds for Gauss sums derived from $$k$$th powers, and for Heilbronn’s exponential sum. Zbl 0983.11052
Heath-Brown, D. R.; Konyagin, S.
2000
The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Zbl 0815.11032
Heath-Brown, D. R.
1994
The twelfth power moment of the Riemann-function. Zbl 0394.10020
Heath-Brown, D. R.
1978
Integer sets containing no arithmetic progressions. Zbl 0589.10062
Heath-Brown, D. R.
1987
A mean value estimate for real character sums. Zbl 0828.11040
Heath-Brown, D. R.
1995
A new form of the circle method, and its application to quadratic forms. Zbl 0857.11049
Heath-Brown, D. R.
1996
The distribution and moments of the error term in the Dirichlet divisor problems. Zbl 0725.11045
Heath-Brown, D. R.
1992
Lattice points in the sphere. Zbl 0929.11040
Heath-Brown, D. R.
1999
Fractional moments of the Riemann zeta-function. Zbl 0431.10024
Heath-Brown, D. R.
1981
Cubic forms in 10 variables. Zbl 0494.10012
Heath-Brown, D. R.
1983
The square sieve and consecutive square-free numbers. Zbl 0514.10038
Heath-Brown, D. R.
1984
Integers represented as a sum of primes and powers of two. Zbl 1097.11050
Heath-Brown, D. R.; Puchta, J.-C.
2002
Hybrid bounds for Dirichlet L-functions. Zbl 0362.10035
Heath-Brown, D. R.
1978
The size of Selmer groups for the congruent number problem. Zbl 0808.11041
Heath-Brown, D. R.
1993
The distribution of Kummer sums at prime arguments. Zbl 0412.10028
Heath-Brown, D. R.; Patterson, S. J.
1979
Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. Zbl 0549.10030
Balasubramanian, R.; Conrey, J. B.; Heath-Brown, D. R.
1985
The number of primes in a short interval. Zbl 0646.10032
Heath-Brown, D. R.
1988
On the difference between consecutive primes. Zbl 0424.10028
Heath-Brown, D. R.; Iwaniec, H.
1979
Pair correlation for fractional parts of $$\alpha n^2$$. Zbl 1239.11081
Heath-Brown, D. R.
2010
Hybrid bounds for Dirichlet L-functions. II. Zbl 0396.10030
Heath-Brown, D. R.
1980
Diophantine approximation with square-free numbers. Zbl 0539.10026
Heath-Brown, D. R.
1984
The divisor function $$d_ 3(n)$$ in arithmetic progressions. Zbl 0549.10034
Heath-Brown, D. R.
1986
Simple zeros of the Riemann zeta-function on the critical line. Zbl 0409.10027
Heath-Brown, D. R.
1979
Cubic forms in 14 variables. Zbl 1135.11031
Heath-Brown, D. R.
2007
Almost-primes in arithmetic progressions and short intervals. Zbl 0375.10027
Heath-Brown, D. R.
1978
Weyl’s inequality, Hua’s inequality and Waring’s problem. Zbl 0619.10046
Heath-Brown, D. R.
1988
The growth rate of the Dedekind zeta-function on the critical line. Zbl 0583.12011
Heath-Brown, D. R.
1988
Gaps between primes, and the pair correlation of zeros of the zeta-function. Zbl 0414.10044
Heath-Brown, D. R.
1982
The density of rational points on cubic surfaces. Zbl 0863.11021
Heath-Brown, D. R.
1997
Primes represented by $$x^3+ 2y^3$$. Zbl 1007.11055
Heath-Brown, D. R.
2001
Prime twins and Siegel zeros. Zbl 0517.10044
Heath-Brown, D. R.
1983
Counting rational points on algebraic varieties. Zbl 1098.14013
Browning, T. D.; Heath-Brown, D. R.; Salberger, P.
2006
An estimate for Heilbronn’s exponential sum. Zbl 0857.11041
Heath-Brown, D. R.
1996
The divisor function at consecutive integers. Zbl 0529.10040
Heath-Brown, D. R.
1984
Sign changes of $$E(T)$$, $$\Delta(x)$$, and $$P(x)$$. Zbl 0810.11046
Heath-Brown, D. R.; Tsang, K.-M.
1994
The average analytic rank of elliptic curves. Zbl 1063.11013
Heath-Brown, D. R.
2004
The fourth power mean of Dirichlet’s L-functions. Zbl 0479.10027
Heath-Brown, D. R.
1981
The distribution of $$\alpha p$$ modulo one. Zbl 1023.11034
Heath-Brown, D. R.; Jia, Chaohua
2002
Counting rational points on hypersurfaces. Zbl 1079.11033
Browning, T. D.; Heath-Brown, D. R.
2005
Small solutions of quadratic congruences. Zbl 0581.10008
Heath-Brown, D. R.
1985
The least square-free number in an arithmetic progression. Zbl 0493.10045
Heath-Brown, D. R.
1982
Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006
Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E.
2008
Rational solutions of certain equations involving norms. Zbl 1023.11033
Heath-Brown, Roger; Skorobogatov, Alexei
2002
An asymptotic series for the mean value of Dirichlet $$L$$-functions. Zbl 0457.10020
Heath-Brown, D. R.
1981
Counting rational points on algebraic varieties. Zbl 1152.11027
Heath-Brown, D. R.
2006
Odd perfect numbers. Zbl 0805.11005
Heath-Brown, D. R.
1994
On the density of the zeros of the Dedekind zeta-function. Zbl 0325.12003
Heath-Brown, D. R.
1977
On the distribution of gaps between zeros of the zeta-function. Zbl 0557.10028
Conrey, J. B.; Ghosh, A.; Goldston, D.; Gonek, S. M.; Heath-Brown, D. R.
1985
The first case of Fermat’s last theorem. Zbl 0557.10034
Adleman, L. M.; Heath-Brown, D. R.
1985
Forms in many variables and differing degrees. Zbl 1383.11039
Browning, Tim; Heath-Brown, Roger
2017
Almost-prime $$k$$-tuples. Zbl 0886.11052
Heath-Brown, D. R.
1997
Lagrange’s four squares theorem with one prime and three almost-prime variables. Zbl 1022.11050
Heath-Brown, D. R.; Tolev, D. I.
2003
Fractional moments of the Riemann zeta-function. II. Zbl 0798.11031
Heath-Brown, D. R.
1993
Kummer’s conjecture for cubic Gauss sums. Zbl 0989.11042
Heath-Brown, D. R.
2000
A new $$k$$th derivative estimate for exponential sums via Vinogradov’s mean value. Zbl 1461.11110
Heath-Brown, D. R.
2017
The differences between consecutive primes. Zbl 0387.10025
Heath-Brown, D. R.
1978
On simple zeros of the Riemann zeta-function. Zbl 1291.11118
Bui, H. M.; Heath-Brown, D. R.
2013
Zero-free regions for Dirichlet $$L$$-functions and the least prime in an arithmetic progression. Zbl 0725.11041
Heath-Brown, D. R.
1992
The circle method and diagonal cubic forms. Zbl 0899.11051
Heath-Brown, D. R.
1998
Three primes and an almost-prime in arithmetic progression. Zbl 0425.10051
Heath-Brown, D. R.
1981
Imaginary quadratic fields with class group exponent 5. Zbl 1268.11150
Heath-Brown, D. R.
2008
Primes represented by binary cubic forms. Zbl 1030.11046
Heath-Brown, D. R.; Moroz, B. Z.
2002
The density of rational points on non-singular hypersurfaces. Zbl 0808.11042
Heath-Brown, D. R.
1994
On the representation of primes by cubic polynomials in two variables. Zbl 1099.11050
Heath-Brown, D. R.; Moroz, B. Z.
2004
Irreducible polynomials over finite fields produced by composition of quadratics. Zbl 07083114
Heath-Brown, David Rodney; Micheli, Giacomo
2019
Zero density estimates for the Riemann zeta-function and Dirichlet L-functions. Zbl 0393.10043
Heath-Brown, D. R.
1979
The differences between consecutive primes. II. Zbl 0394.10021
Heath-Brown, D. R.
1979
Rational points on quartic hypersurfaces. Zbl 1169.11027
Browning, T. D.; Heath-Brown, D. R.
2009
Burgess’s bounds for character sums. Zbl 1328.11088
Heath-Brown, D. R.
2013
Almost-primes in short intervals. Zbl 0461.10041
Halberstam, H.; Heath-Brown, D. R.; Richert, H.-E.
1981
Siegel zeros and the least prime in an arithmetic progression. Zbl 0715.11049
Heath-Brown, D. R.
1990
A note on the differences between consecutive primes. Zbl 0514.10031
Heath-Brown, D. R.; Goldston, D. A.
1984
The density of zeros of forms for which weak approximation fails. Zbl 0778.11017
Heath-Brown, D. R.
1992
Zeros of systems of $$\mathfrak p$$-adic quadratic forms. Zbl 1194.11047
Heath-Brown, D. R.
2010
On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055
Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E.
2005
The density of rational points on Cayley’s cubic surface. Zbl 1060.11038
Heath-Brown, D. R.
2003
The density of rational points on the cubic surface $$X_0^3=X_1X_2X_3$$. Zbl 0938.11016
Heath-Brown, D. R.; Moroz, B. Z.
1999
Burgess bounds for short mixed character sums. Zbl 1317.11083
Heath-Brown, D. R.; Pierce, L. B.
2015
Zeros of $$p$$-adic forms. Zbl 1233.11039
Heath-Brown, D. R.
2010
The mean value theorem for the Riemann zeta-function. Zbl 0387.10023
Heath-Brown, D. R.
1979
Quadratic polynomials represented by norm forms. Zbl 1264.14032
Browning, T. D.; Heath-Brown, D. R.
2012
Power-free values of polynomials. Zbl 1287.11114
Heath-Brown, D. R.
2013
Simultaneous integer values of pairs of quadratic forms. Zbl 1396.11121
Heath-Brown, D. R.; Pierce, L. B.
2017
The ternary Goldbach problem. Zbl 0599.10041
Heath-Brown, D. R.
1985
Exponential sums with a difference. Zbl 0675.10027
Heath-Brown, D. R.; Huxley, M. N.
1990
Mean values of the zeta-function and divisor problems. Zbl 0457.10019
Heath-Brown, D. R.
1981
The differences between consecutive primes. III. Zbl 0407.10032
Heath-Brown, D. R.
1979
Every sum of cubes in $$\mathbb F_2[t]$$ is a strict sum of 6 cubes. Zbl 1172.11045
Gallardo, Luis H.; Heath-Brown, D. R.
2007
Quadratic class numbers divisible by 3. Zbl 1140.11050
Heath-Brown, D. Roger
2007
The density of rational points on non-singular hypersurfaces. II. (With an appendix by J. M. Starr). Zbl 1104.11015
Browning, T. D.; Heath-Brown, D. R.; Starr, J. M.
2006
The largest prime factor of $$X^3+2$$. Zbl 1023.11048
Heath-Brown, D. R.
2001
On solving the diophantine equation $$x^ 3+y^ 3+z^ 3=k$$ on a vector computer. Zbl 0783.11046
Heath-Brown, D. R.; Lioen, W. M.; te Riele, Herman J. J.
1993
A note on the Chevalley-Warning theorems. Zbl 1247.11089
Heath-Brown, D. R.
2011
Integral points on cubic hypersurfaces. Zbl 1244.11066
Browning, T. D.; Heath-Brown, D. R.
2009
Irreducible polynomials over finite fields produced by composition of quadratics. Zbl 07083114
Heath-Brown, David Rodney; Micheli, Giacomo
2019
Counting rational points on quadric surfaces. Zbl 1444.11142
Browning, T. D.; Heath-Brown, D. R.
2018
The differences between consecutive smooth numbers. Zbl 1446.11173
Heath-Brown, D. R.
2018
Forms in many variables and differing degrees. Zbl 1383.11039
Browning, Tim; Heath-Brown, Roger
2017
A new $$k$$th derivative estimate for exponential sums via Vinogradov’s mean value. Zbl 1461.11110
Heath-Brown, D. R.
2017
Simultaneous integer values of pairs of quadratic forms. Zbl 1396.11121
Heath-Brown, D. R.; Pierce, L. B.
2017
Averages and moments associated to class numbers of imaginary quadratic fields. Zbl 1391.11151
Heath-Brown, D. R.; Pierce, L. B.
2017
Prime values of $$a^2 + p^4$$. Zbl 1405.11124
Heath-Brown, D. R.; Li, Xiannan
2017
Iteration of quadratic polynomials over finite fields. Zbl 1428.11204
Heath-Brown, D. R.
2017
Almost prime triples and Chen’s theorem. Zbl 1390.11109
Heath-Brown, Roger; Li, Xiannan
2016
Small solutions of quadratic congruences, and character sums with binary quadratic forms. Zbl 1375.11036
Heath-Brown, D. R.
2016
Burgess bounds for short mixed character sums. Zbl 1317.11083
Heath-Brown, D. R.; Pierce, L. B.
2015
Rational points on intersections of cubic and quadric hypersurfaces. Zbl 1327.11043
Browning, T. D.; Dietmann, R.; Heath-Brown, D. R.
2015
Large gaps between consecutive prime numbers containing perfect powers. Zbl 1391.11125
Ford, Kevin; Heath-Brown, D. R.; Konyagin, Sergei
2015
On simple zeros of the Riemann zeta-function. Zbl 1291.11118
Bui, H. M.; Heath-Brown, D. R.
2013
Burgess’s bounds for character sums. Zbl 1328.11088
Heath-Brown, D. R.
2013
Power-free values of polynomials. Zbl 1287.11114
Heath-Brown, D. R.
2013
$$p$$-adic zeros of systems of quadratic forms. Zbl 1333.11036
Heath-Brown, D. R.
2013
Quadratic polynomials represented by norm forms. Zbl 1264.14032
Browning, T. D.; Heath-Brown, D. R.
2012
Square-free values of $$n^2+1$$. Zbl 1312.11077
Heath-Brown, D. R.
2012
Counting rational points on smooth cyclic covers. Zbl 1248.14027
Heath-Brown, D. R.; Pierce, Lillian B.
2012
A note on the Chevalley-Warning theorems. Zbl 1247.11089
Heath-Brown, D. R.
2011
Pair correlation for fractional parts of $$\alpha n^2$$. Zbl 1239.11081
Heath-Brown, D. R.
2010
Zeros of systems of $$\mathfrak p$$-adic quadratic forms. Zbl 1194.11047
Heath-Brown, D. R.
2010
Zeros of $$p$$-adic forms. Zbl 1233.11039
Heath-Brown, D. R.
2010
Fractional moments of Dirichlet $$L$$-functions. Zbl 1248.11059
Heath-Brown, D. R.
2010
A note on the fourth moment of Dirichlet $$L$$-functions. Zbl 1203.11056
Bui, H. M.; Heath-Brown, D. R.
2010
Bounds for the cubic Weyl sum. Zbl 1282.11102
Heath-Brown, D. R.
2010
Counting rational points on cubic curves. Zbl 1229.11052
Heath-Brown, Roger; Testa, Damiano
2010
Rational points on quartic hypersurfaces. Zbl 1169.11027
Browning, T. D.; Heath-Brown, D. R.
2009
Integral points on cubic hypersurfaces. Zbl 1244.11066
Browning, T. D.; Heath-Brown, D. R.
2009
Sums and differences of three $$k$$th powers. Zbl 1182.11017
Heath-Brown, D. R.
2009
Convexity bounds for $$L$$-functions. Zbl 1169.11038
Heath-Brown, D. R.
2009
Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006
Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E.
2008
Imaginary quadratic fields with class group exponent 5. Zbl 1268.11150
Heath-Brown, D. R.
2008
Cubic forms in 14 variables. Zbl 1135.11031
Heath-Brown, D. R.
2007
Every sum of cubes in $$\mathbb F_2[t]$$ is a strict sum of 6 cubes. Zbl 1172.11045
Gallardo, Luis H.; Heath-Brown, D. R.
2007
Quadratic class numbers divisible by 3. Zbl 1140.11050
Heath-Brown, D. Roger
2007
Analytic methods for the distribution of rational points of algebraic varieties. Zbl 1181.11042
Heath-Brown, D. R.
2007
Carmichael numbers with three prime factors. Zbl 1151.11047
Heath-Brown, D. R.
2007
A note on the 2-part of $$\text{Ш}$$ for the congruent number curves. Zbl 1216.11062
Heath-Brown, D. R.
2007
Counting rational points on algebraic varieties. Zbl 1098.14013
Browning, T. D.; Heath-Brown, D. R.; Salberger, P.
2006
Counting rational points on algebraic varieties. Zbl 1152.11027
Heath-Brown, D. R.
2006
The density of rational points on non-singular hypersurfaces. II. (With an appendix by J. M. Starr). Zbl 1104.11015
Browning, T. D.; Heath-Brown, D. R.; Starr, J. M.
2006
The density of rational points on non-singular hypersurfaces. I. Zbl 1174.11051
Browning, T. D.; Heath-Brown, D. R.
2006
Counting rational points on hypersurfaces. Zbl 1079.11033
Browning, T. D.; Heath-Brown, D. R.
2005
On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055
Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E.
2005
Plane curves in boxes and equal sums of two powers. Zbl 1174.11380
Browning, T. D.; Heath-Brown, D. R.
2005
Permutation groups, simple groups, and sieve methods. Zbl 1091.11035
Heath-Brown, D. R.; Praeger, Cheryl E.; Shalev, Aner
2005
Prime number theory and the Riemann zeta-function. Zbl 1204.11144
Heath-Brown, D. R.
2005
The average analytic rank of elliptic curves. Zbl 1063.11013
Heath-Brown, D. R.
2004
On the representation of primes by cubic polynomials in two variables. Zbl 1099.11050
Heath-Brown, D. R.; Moroz, B. Z.
2004
Equal sums of three powers. Zbl 1135.11052
Browning, T. D.; Heath-Brown, D. R.
2004
Lagrange’s four squares theorem with one prime and three almost-prime variables. Zbl 1022.11050
Heath-Brown, D. R.; Tolev, D. I.
2003
The density of rational points on Cayley’s cubic surface. Zbl 1060.11038
Heath-Brown, D. R.
2003
Linear relations amongst sums of two squares. Zbl 1161.11387
Heath-Brown, D. R.
2003
Proceedings of the session in analytic number theory and Diophantine equations held in Bonn, Germany, January–June, 2002. Zbl 1050.11003
Heath-Brown, D. R.; Moroz, B. Z.
2003
Lectures on sieves. Zbl 1070.11045
Heath-Brown, D. R.
2003
The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène). Zbl 1039.11044
Heath-Brown, D. R.
2002
Integers represented as a sum of primes and powers of two. Zbl 1097.11050
Heath-Brown, D. R.; Puchta, J.-C.
2002
The distribution of $$\alpha p$$ modulo one. Zbl 1023.11034
Heath-Brown, D. R.; Jia, Chaohua
2002
Rational solutions of certain equations involving norms. Zbl 1023.11033
Heath-Brown, Roger; Skorobogatov, Alexei
2002
Primes represented by binary cubic forms. Zbl 1030.11046
Heath-Brown, D. R.; Moroz, B. Z.
2002
Heilbronn’s exponential sum and transcendence theory. Zbl 1177.11072
Heath-Brown, D. R.
2002
Primes represented by $$x^3+ 2y^3$$. Zbl 1007.11055
Heath-Brown, D. R.
2001
The largest prime factor of $$X^3+2$$. Zbl 1023.11048
Heath-Brown, D. R.
2001
New bounds for Gauss sums derived from $$k$$th powers, and for Heilbronn’s exponential sum. Zbl 0983.11052
Heath-Brown, D. R.; Konyagin, S.
2000
Kummer’s conjecture for cubic Gauss sums. Zbl 0989.11042
Heath-Brown, D. R.
2000
Arithmetic applications of Kloosterman sums. Zbl 1173.11339
Heath-Brown, D. R.
2000
Exponential decay in the frequency of analytic ranks of automorphic $$L$$-functions. Zbl 1166.11326
Heath-Brown, D. R.; Michel, P.
2000
Lattice points in the sphere. Zbl 0929.11040
Heath-Brown, D. R.
1999
The density of rational points on the cubic surface $$X_0^3=X_1X_2X_3$$. Zbl 0938.11016
Heath-Brown, D. R.; Moroz, B. Z.
1999
The solubility of diagonal cubic Diophantine equations. Zbl 1029.11010
Heath-Brown, D. R.
1999
A note on the paper ‘consecutive almost-primes’. Zbl 1141.11318
Heath-Brown, D. R.
1999
The circle method and diagonal cubic forms. Zbl 0899.11051
Heath-Brown, D. R.
1998
The largest prime factor of the integers in an interval. II. Zbl 1066.11506
Heath-Brown, D. R.; Jia, Chaohua
1998
Counting rational points on cubic surfaces. Zbl 0926.11046
Heath-Brown, Roger
1998
The density of rational points on cubic surfaces. Zbl 0863.11021
Heath-Brown, D. R.
1997
Almost-prime $$k$$-tuples. Zbl 0886.11052
Heath-Brown, D. R.
1997
A new form of the circle method, and its application to quadratic forms. Zbl 0857.11049
Heath-Brown, D. R.
1996
An estimate for Heilbronn’s exponential sum. Zbl 0857.11041
Heath-Brown, D. R.
1996
The largest prime factor of the integers in an interval. Zbl 0867.11064
Heath-Brown, D. R.
1996
A mean value estimate for real character sums. Zbl 0828.11040
Heath-Brown, D. R.
1995
The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Zbl 0815.11032
Heath-Brown, D. R.
1994
Sign changes of $$E(T)$$, $$\Delta(x)$$, and $$P(x)$$. Zbl 0810.11046
Heath-Brown, D. R.; Tsang, K.-M.
1994
Odd perfect numbers. Zbl 0805.11005
Heath-Brown, D. R.
1994
The density of rational points on non-singular hypersurfaces. Zbl 0808.11042
Heath-Brown, D. R.
1994
The size of Selmer groups for the congruent number problem. Zbl 0808.11041
Heath-Brown, D. R.
1993
Fractional moments of the Riemann zeta-function. II. Zbl 0798.11031
Heath-Brown, D. R.
1993
On solving the diophantine equation $$x^ 3+y^ 3+z^ 3=k$$ on a vector computer. Zbl 0783.11046
Heath-Brown, D. R.; Lioen, W. M.; te Riele, Herman J. J.
1993
The Dirichlet divisor problem. Zbl 0791.11048
Heath-Brown, D. R.
1993
Zero-free regions for Dirichlet $$L$$-functions and the least prime in an arithmetic progression. Zbl 0739.11033
Heath-Brown, D. R.
1992
The distribution and moments of the error term in the Dirichlet divisor problems. Zbl 0725.11045
Heath-Brown, D. R.
1992
Zero-free regions for Dirichlet $$L$$-functions and the least prime in an arithmetic progression. Zbl 0725.11041
Heath-Brown, D. R.
1992
The density of zeros of forms for which weak approximation fails. Zbl 0778.11017
Heath-Brown, D. R.
1992
Calabi-Yau threefolds with $$\rho > 13$$. Zbl 0759.14030
Heath-Brown, D. R.; Wilson, P. M. H.
1992
Zero-free regions of $$\zeta (s)$$ and $$L(s,\chi)$$. Zbl 0791.11042
Heath-Brown, D. R.
1992
Searching for solutions of $$x^ 3+y^ 3+z^ 3=k$$. Zbl 0745.11023
Heath-Brown, D. R.
1992
Small solutions of quadratic congruences. II. Zbl 0725.11018
Heath-Brown, D. R.
1991
Square-full numbers in short intervals. Zbl 0735.11043
Heath-Brown, D. R.
1991
...and 60 more Documents
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#### Cited by 1,173 Authors

 56 Shparlinski, Igor E. 34 Browning, Timothy Daniel 32 Heath-Brown, Roger 23 Zhai, Wenguang 20 Wooley, Trevor D. 19 Ivić, Aleksandar P. 19 Lu, Guangshi 17 Harman, Glyn 15 Zaharescu, Alexandru 14 Iwaniec, Henryk 14 Michel, Philippe Gabriel 13 Baker, Roger C. 12 Banks, William D. 12 Brüdern, Jörg 12 Fouvry, Etienne 12 Goldston, Daniel Alan 12 Tsang, Kai-Man 11 Blomer, Valentin 11 Bourgain, Jean 11 Cao, Xiaodong 11 de la Bretèche, Régis 11 Soundararajan, Kannan 11 Tao, Terence 10 Baier, Stephan 10 Cai, Yingchun 10 Cochrane, Todd 10 Li, Jinjiang 10 Liu, Zhixin 10 Murty, Maruti Ram 10 Perelli, Alberto 9 Bazzanella, Danilo 9 Conrey, John Brian 9 Dietmann, Rainer 9 Garaev, Moubariz Z. 9 Kowalski, Emmanuel 9 Laurinčikas, Antanas 9 Munshi, Ritabrata 9 Pierce, Lillian B. 9 Pintz, Janos 9 Tanigawa, Yoshio 9 Young, Matthew P. 9 Zhang, Min 8 Chang, Mei-Chu 8 Fomenko, Oleg Mstislavovich 8 Hu, Liqun 8 Konyagin, Sergeĭ Vladimirovich 8 Lau, Yuk-Kam 8 Pollack, Paul 8 Sankaranarayanan, Ayyadurai 8 Shkredov, Il’ya Dmitrievich 8 Zhao, Liangyi 7 Chamizo Lorente, Fernando 7 Derenthal, Ulrich 7 Ford, Kevin B. 7 Friedlander, John Benjamin 7 Korolëv, Maksim Aleksandrovich 7 Kumchev, Angel V. 7 Luca, Florian 7 Maynard, James 7 Nowak, Werner Georg 7 Radziwiłł, Maksym 7 Robles, Nicolas 6 Aistleitner, Christoph 6 Jutila, Matti Ilmari 6 Lamzouri, Youness 6 Liu, Huafeng 6 Motohashi, Yoichi 6 Rassias, Michael Th. 6 Rubin, Karl Cooper 6 Salberger, Per 6 Sarnak, Peter Clive 6 Sofos, Efthymios 6 Steuding, Jörn 6 Sun, Haiwei 6 Tolev, Doychin I. 6 Vaughan, Robert C. 6 Wu, Jie 6 Xiao, Stanley Yao 6 Zhao, Lilu 5 Bettin, Sandro 5 Furuya, Jun 5 Gao, Peng 5 Garcia, Stephan Ramon 5 Katsurada, Masanori 5 Klagsbrun, Zev 5 Larcher, Gerhard 5 Maier, Helmut 5 Marmon, Oscar 5 Matomäki, Kaisa Sofia 5 Mazur, Barry 5 Milinovich, Micah B. 5 Munsch, Marc 5 Parsell, Scott T. 5 Rivat, Joël 5 Rudnick, Zeév 5 Sawin, William F. 5 Sono, Keiju 5 Spencer, Craig V. 5 Wood, Melanie Matchett 5 Xi, Ping ...and 1,073 more Authors
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#### Cited in 199 Serials

 185 Journal of Number Theory 72 Mathematika 51 International Journal of Number Theory 38 Mathematics of Computation 37 Journal de Théorie des Nombres de Bordeaux 35 Acta Arithmetica 35 Proceedings of the American Mathematical Society 34 Duke Mathematical Journal 34 Monatshefte für Mathematik 32 Transactions of the American Mathematical Society 29 Mathematische Zeitschrift 28 Mathematische Annalen 25 Functiones et Approximatio. Commentarii Mathematici 25 Acta Mathematica Hungarica 24 Mathematical Proceedings of the Cambridge Philosophical Society 23 The Ramanujan Journal 22 Inventiones Mathematicae 22 Journal für die Reine und Angewandte Mathematik 21 Lithuanian Mathematical Journal 21 Advances in Mathematics 19 Rocky Mountain Journal of Mathematics 19 Annals of Mathematics. Second Series 18 Israel Journal of Mathematics 17 Mathematical Notes 17 Compositio Mathematica 16 Bulletin of the American Mathematical Society. New Series 15 Bulletin of the Australian Mathematical Society 14 Archiv der Mathematik 13 Acta Mathematica Sinica. New Series 13 Research in Number Theory 12 Journal of Mathematical Analysis and Applications 12 Michigan Mathematical Journal 12 Forum Mathematicum 12 Journal of Mathematical Sciences (New York) 12 Science China. Mathematics 11 Finite Fields and their Applications 10 Journal d’Analyse Mathématique 10 Proceedings of the London Mathematical Society. Third Series 10 Geometric and Functional Analysis. GAFA 10 Algebra & Number Theory 9 Discrete Mathematics 9 Proceedings of the Japan Academy. Series A 9 Journal of the American Mathematical Society 9 Indagationes Mathematicae. New Series 9 Chebyshevskiĭ Sbornik 8 Bulletin of the London Mathematical Society 8 Glasgow Mathematical Journal 8 Manuscripta Mathematica 8 Central European Journal of Mathematics 8 Proceedings of the Steklov Institute of Mathematics 7 Annales de l’Institut Fourier 7 Journal of the London Mathematical Society. Second Series 7 Integers 6 Communications in Mathematical Physics 6 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 6 Revista Matemática Iberoamericana 6 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 6 Experimental Mathematics 6 Journal of the European Mathematical Society (JEMS) 6 Acta Mathematica Sinica. English Series 6 Journal of the Australian Mathematical Society 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Frontiers of Mathematics in China 6 Forum of Mathematics, Sigma 5 Periodica Mathematica Hungarica 5 The Mathematical Intelligencer 5 Journal of Soviet Mathematics 5 Designs, Codes and Cryptography 5 Expositiones Mathematicae 4 Acta Mathematica 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Canadian Journal of Mathematics 4 Journal of Algebra 4 Journal of Combinatorial Theory. Series A 4 Chinese Annals of Mathematics. Series B 4 Journal of Complexity 4 Science in China. Series A 4 Sbornik: Mathematics 4 Portugaliae Mathematica. Nova Série 3 American Mathematical Monthly 3 Mathematische Semesterberichte 3 Arkiv för Matematik 3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Applied Mathematics and Computation 3 Commentarii Mathematici Helvetici 3 Journal of Functional Analysis 3 Rendiconti del Seminario Matematico della Università di Padova 3 Theoretical Computer Science 3 St. Petersburg Mathematical Journal 3 Selecta Mathematica. New Series 3 Journal of the Institute of Mathematics of Jussieu 3 Journal of Algebra and its Applications 3 Cryptography and Communications 3 Forum of Mathematics, Pi 3 Research in the Mathematical Sciences 2 Archive for History of Exact Sciences 2 Information Processing Letters 2 The Mathematical Gazette 2 Czechoslovak Mathematical Journal 2 Journal of Computer and System Sciences ...and 99 more Serials
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#### Cited in 47 Fields

 1,418 Number theory (11-XX) 165 Algebraic geometry (14-XX) 42 Combinatorics (05-XX) 30 Group theory and generalizations (20-XX) 25 Information and communication theory, circuits (94-XX) 24 Dynamical systems and ergodic theory (37-XX) 22 Harmonic analysis on Euclidean spaces (42-XX) 19 Probability theory and stochastic processes (60-XX) 18 Convex and discrete geometry (52-XX) 18 Computer science (68-XX) 16 Partial differential equations (35-XX) 14 Field theory and polynomials (12-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 History and biography (01-XX) 10 Topological groups, Lie groups (22-XX) 9 Functions of a complex variable (30-XX) 9 Numerical analysis (65-XX) 8 Measure and integration (28-XX) 8 Several complex variables and analytic spaces (32-XX) 7 Mathematical logic and foundations (03-XX) 7 Special functions (33-XX) 7 Quantum theory (81-XX) 6 Approximations and expansions (41-XX) 6 Geometry (51-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 General and overarching topics; collections (00-XX) 4 Commutative algebra (13-XX) 4 Associative rings and algebras (16-XX) 4 Real functions (26-XX) 4 Abstract harmonic analysis (43-XX) 4 Differential geometry (53-XX) 3 Statistics (62-XX) 2 $$K$$-theory (19-XX) 2 Potential theory (31-XX) 2 Operator theory (47-XX) 2 Operations research, mathematical programming (90-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Nonassociative rings and algebras (17-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Manifolds and cell complexes (57-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX)

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