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## van Frankenhuijsen, Machiel

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 Author ID: van-frankenhuijsen.machiel Published as: Van Frankenhuysen, Machiel; van Frankenhuijsen, Machiel; van Frankenhuysen, Machiel Homepage: http://research.uvu.edu/machiel/ External Links: MGP · Wikidata · GND
 Documents Indexed: 26 Publications since 1999, including 9 Books Reviewing Activity: 2 Reviews

#### Co-Authors

 11 single-authored 13 Lapidus, Michel L. 2 Carfì, David 2 Laca, Marcelo 2 Pearse, Erin Peter James 1 Hùng, Lũ’
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#### Serials

 5 Journal of Number Theory 3 Contemporary Mathematics 2 Proceedings of Symposia in Pure Mathematics 2 Springer Monographs in Mathematics 1 Journal für die Reine und Angewandte Mathematik 1 Expositiones Mathematicae 1 Experimental Mathematics 1 Matemática Contemporânea 1 London Mathematical Society Student Texts
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#### Fields

 23 Number theory (11-XX) 13 Measure and integration (28-XX) 11 Dynamical systems and ergodic theory (37-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 General and overarching topics; collections (00-XX) 4 Algebraic geometry (14-XX) 3 Functions of a complex variable (30-XX) 3 Quantum theory (81-XX) 2 Ordinary differential equations (34-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Probability theory and stochastic processes (60-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

20 Publications have been cited 201 times in 136 Documents Cited by Year
Fractal geometry and number theory. Complex dimensions of fractal strings and zeros of zeta functions. Zbl 0981.28005
Lapidus, Michel L.; van Frankenhuysen, Machiel
2000
Fractal geometry, complex dimensions and zeta functions. Geometry and spectra of fractal strings. Zbl 1119.28005
Lapidus, Michel L.; van Frankenhuijsen, Machiel
2006
Fractal geometry, complex dimensions and zeta functions. Geometry and spectra of fractal strings. 2nd ed. Zbl 1261.28011
Lapidus, Michel L.; van Frankenhuijsen, Machiel
2013
Phase transitions on Hecke $$C^*$$-algebras and class-field theory over $$\mathbb Q$$. Zbl 1136.11070
Laca, Marcelo; van Frankenhuijsen, Machiel
2006
Complex dimensions of self-similar fractal strings and Diophantine approximation. Zbl 1061.11039
Lapidus, Michel L.; van Frankenhuysen, Machiel
2003
Arithmetic progressions of zeros of the Riemann zeta function. Zbl 1087.11054
van Frankenhuijsen, Machiel
2005
A lower bound in the $$abc$$ conjecture. Zbl 0998.11033
van Frankenhuysen, Machiel
2000
Fractality, self-similarity and complex dimensions. Zbl 1196.11100
Lapidus, Michel L.; van Frankenhuijsen, Machiel
2004
ABC implies the radicalized Vojta height inequality for curves. Zbl 1197.11087
van Frankenhuijsen, Machiel
2007
Complex dimensions of fractal strings and oscillatory phenomena in fractal geometry and arithmetic. Zbl 0945.11016
Lapidus, Michel L.; van Frankenhuysen, Machiel
1999
Fractal geometry and dynamical systems in pure and applied mathematics I: Fractals in pure mathematics. Selected papers based on three conferences following the passing of Benoît Mandelbrot in October 2010. 1st PISRS 2011 international conference on analysis, fractal geometry, dynamical systems and economics, Messina, Italy, November 8–12, 2011, AMS special session on fractal geometry in pure and applied mathematics, in memory of Benoît Mandelbrot, Boston, MA, USA, January 2012, AMS special session on geometry and analysis on fractal spaces, Honolulu, HI, USA, March 2012. Zbl 1276.00022
Carfì, David (ed.); Lapidus, Michel L. (ed.); Pearse, Erin P. J. (ed.); van Frankenhuijsen, Machiel (ed.)
2013
The ABC conjecture implies Roth’s theorem and Mordell’s conjecture. Zbl 0977.11016
van Frankenhuysen, Machiel
1999
Minkowski measurability and exact fractal tube formulas for $$p$$-adic self-similar strings. Zbl 1321.37081
Lapidus, Michel L.; Hùng, Lũ’; van Frankenhuijsen, Machiel
2013
The ABC conjecture implies Vojta’s height inequality for curves. Zbl 1083.11042
Van Frankenhuysen, Machiel
2002
The Riemann hypothesis for function fields. Frobenius flow and shift operators. Zbl 1294.14009
van Frankenhuijsen, Machiel
2014
About the ABC conjecture and an alternative. Zbl 1267.11034
van Frankenhuijsen, Machiel
2012
Riemann zeros in arithmetic progression. Zbl 1325.11088
van Frankenhuijsen, Machiel
2013
Phase transitions with spontaneous symmetry breaking on Hecke $$C^*$$-algebras from number fields. Zbl 1105.11037
Laca, Marcelo; van Frankenhuijsen, Machiel
2006
Fractal geometry and applications: A jubilee of Benoît Mandelbrot. Multifractals, probability and statistical mechanics, applications. In part the proceedings of a special session held during the annual meeting of the American Mathematical Society, San Diego, CA, USA, January 2002. Zbl 1055.37003
Lapidus, Michel L. (ed.); van Frankenhuijsen, Machiel (ed.)
2004
A prime orbit theorems for self-similar flows and Diophantine approximation. Zbl 1107.37008
Lapidus, Michel L.; van Frankenhuysen, Machiel
2001
The Riemann hypothesis for function fields. Frobenius flow and shift operators. Zbl 1294.14009
van Frankenhuijsen, Machiel
2014
Fractal geometry, complex dimensions and zeta functions. Geometry and spectra of fractal strings. 2nd ed. Zbl 1261.28011
Lapidus, Michel L.; van Frankenhuijsen, Machiel
2013
Fractal geometry and dynamical systems in pure and applied mathematics I: Fractals in pure mathematics. Selected papers based on three conferences following the passing of Benoît Mandelbrot in October 2010. 1st PISRS 2011 international conference on analysis, fractal geometry, dynamical systems and economics, Messina, Italy, November 8–12, 2011, AMS special session on fractal geometry in pure and applied mathematics, in memory of Benoît Mandelbrot, Boston, MA, USA, January 2012, AMS special session on geometry and analysis on fractal spaces, Honolulu, HI, USA, March 2012. Zbl 1276.00022
Carfì, David (ed.); Lapidus, Michel L. (ed.); Pearse, Erin P. J. (ed.); van Frankenhuijsen, Machiel (ed.)
2013
Minkowski measurability and exact fractal tube formulas for $$p$$-adic self-similar strings. Zbl 1321.37081
Lapidus, Michel L.; Hùng, Lũ’; van Frankenhuijsen, Machiel
2013
Riemann zeros in arithmetic progression. Zbl 1325.11088
van Frankenhuijsen, Machiel
2013
About the ABC conjecture and an alternative. Zbl 1267.11034
van Frankenhuijsen, Machiel
2012
ABC implies the radicalized Vojta height inequality for curves. Zbl 1197.11087
van Frankenhuijsen, Machiel
2007
Fractal geometry, complex dimensions and zeta functions. Geometry and spectra of fractal strings. Zbl 1119.28005
Lapidus, Michel L.; van Frankenhuijsen, Machiel
2006
Phase transitions on Hecke $$C^*$$-algebras and class-field theory over $$\mathbb Q$$. Zbl 1136.11070
Laca, Marcelo; van Frankenhuijsen, Machiel
2006
Phase transitions with spontaneous symmetry breaking on Hecke $$C^*$$-algebras from number fields. Zbl 1105.11037
Laca, Marcelo; van Frankenhuijsen, Machiel
2006
Arithmetic progressions of zeros of the Riemann zeta function. Zbl 1087.11054
van Frankenhuijsen, Machiel
2005
Fractality, self-similarity and complex dimensions. Zbl 1196.11100
Lapidus, Michel L.; van Frankenhuijsen, Machiel
2004
Fractal geometry and applications: A jubilee of Benoît Mandelbrot. Multifractals, probability and statistical mechanics, applications. In part the proceedings of a special session held during the annual meeting of the American Mathematical Society, San Diego, CA, USA, January 2002. Zbl 1055.37003
Lapidus, Michel L. (ed.); van Frankenhuijsen, Machiel (ed.)
2004
Complex dimensions of self-similar fractal strings and Diophantine approximation. Zbl 1061.11039
Lapidus, Michel L.; van Frankenhuysen, Machiel
2003
The ABC conjecture implies Vojta’s height inequality for curves. Zbl 1083.11042
Van Frankenhuysen, Machiel
2002
A prime orbit theorems for self-similar flows and Diophantine approximation. Zbl 1107.37008
Lapidus, Michel L.; van Frankenhuysen, Machiel
2001
Fractal geometry and number theory. Complex dimensions of fractal strings and zeros of zeta functions. Zbl 0981.28005
Lapidus, Michel L.; van Frankenhuysen, Machiel
2000
A lower bound in the $$abc$$ conjecture. Zbl 0998.11033
van Frankenhuysen, Machiel
2000
Complex dimensions of fractal strings and oscillatory phenomena in fractal geometry and arithmetic. Zbl 0945.11016
Lapidus, Michel L.; van Frankenhuysen, Machiel
1999
The ABC conjecture implies Roth’s theorem and Mordell’s conjecture. Zbl 0977.11016
van Frankenhuysen, Machiel
1999
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#### Cited by 172 Authors

 17 Lapidus, Michel L. 9 Žubrinić, Darko 8 Winter, Steffen 7 Laca, Marcelo 7 van Frankenhuijsen, Machiel 6 Kombrink, Sabrina 6 Teplyaev, Alexander 5 Radunović, Goran 5 Županović, Vesna 4 Koçak, Şahin 4 Larsen, Nadia S. 4 Pearse, Erin Peter James 4 Sepulcre, Juan Matias 4 Steuding, Jörn 3 Castro, Carlos 3 Deniz, Ali 3 Guido, Daniele 3 Isola, Tommaso 3 Jørgensen, Palle E. T. 3 Mora, Gaspar 3 Neshveyev, Sergey V. 3 Pašić, Mervan 3 Rock, John A. 3 Üreyen, Adem Ersin 2 Calcagni, Gianluca 2 Chen, Joe Po-Chou 2 Dixit, Atul 2 Dutkay, Dorin Ervin 2 Essouabri, Driss 2 Exel, Ruy 2 Grabner, Peter J. 2 Hambly, Ben M. 2 Kesseböhmer, Marc 2 Korkut, Luka 2 Levin, Aaron 2 Martin, Greg 2 Mijović, V. 2 Olsen, Lars Folke 2 Olsen, Lina Wøhlk 2 Özdemir, Yunus 2 Tanaka, Satoshi 2 Vidal, Tomás 2 Vlah, Domagoj 2 Yasufuku, Yu 2 Zaharescu, Alexandru 1 Albeverio, Sergio A. 1 Allen, Demi 1 Alonso-Ruiz, Patricia 1 Ashbaugh, Mark S. 1 Bailey, David Harold 1 Baumgartner, Udo 1 Bénéteau, Catherine 1 Boava, Giuliano 1 Borwein, Jonathan Michael 1 Cacciapuoti, Claudio 1 Carswell, Brent J. 1 Cesaratto, Eda 1 Charmoy, Philippe H. A. 1 Christensen, Erik 1 Cipriani, Fabio 1 Crandall, Richard E. 1 Crannell, Annalisa 1 Croydon, David A. 1 Cuntz, Joachim 1 Dahmen, Sander R. 1 de Haro, Sebastian 1 Demir, Bunyamin 1 Deninger, Christopher 1 Derfel, Gregory 1 Dettmers, Kristin 1 Dubon, Eric 1 Edwards, Helen J. 1 Eichinger, Tobias 1 El Kaabouchi, Abdelaziz 1 Frame, Michael L. 1 Freiberg, Uta Renata 1 Gatzouras, Dimitris 1 Gesztesy, Fritz 1 Giza, Robert 1 Gupta, N. C. Das 1 Harper, Scott 1 Herichi, Hafedh 1 Hilberdink, Titus W. 1 Hilbert, Lindsay 1 Hille, Martial R. 1 Hinz, Michael 1 Horvat Dmitrović, Lana 1 Humphries, Peter J. 1 Hùng, Lũ’ 1 Ibragimov, Zair 1 Ivan, Cristina 1 Jacob, Benoît 1 Kajino, Naotaka 1 Kelleher, Daniel J. 1 Knill, Oliver 1 Knox, Christina 1 Kouchekian, Sherwin 1 Kozyrev, Sergeĭ Vladimirovich 1 Kühn, Ulf 1 Kumar, Rahul ...and 72 more Authors
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#### Cited in 69 Serials

 12 Journal of Number Theory 8 Advances in Mathematics 8 Transactions of the American Mathematical Society 5 Journal of Mathematical Analysis and Applications 5 Proceedings of the American Mathematical Society 4 Journal of Functional Analysis 4 Fractals 3 Letters in Mathematical Physics 3 Chaos, Solitons and Fractals 3 Applied Mathematics and Computation 3 Acta Applicandae Mathematicae 3 Experimental Mathematics 2 Communications in Mathematical Physics 2 Israel Journal of Mathematics 2 Nuclear Physics. B 2 Functiones et Approximatio. Commentarii Mathematici 2 Journal of Algebra 2 Mathematische Zeitschrift 2 Ergodic Theory and Dynamical Systems 2 Computational Methods and Function Theory 2 Discrete and Continuous Dynamical Systems. Series S 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Journal of Fractal Geometry 1 Advances in Applied Probability 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Journal of Geometry and Physics 1 The Mathematical Intelligencer 1 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Geometriae Dedicata 1 Journal of Approximation Theory 1 Journal of Differential Equations 1 Journal of Geometry 1 Mathematische Annalen 1 Proceedings of the London Mathematical Society. Third Series 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Real Analysis Exchange 1 Physica D 1 Applied Mathematics Letters 1 Forum Mathematicum 1 The Annals of Applied Probability 1 Aequationes Mathematicae 1 Linear Algebra and its Applications 1 Bulletin of the American Mathematical Society. New Series 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Combinatorics, Probability and Computing 1 Bulletin des Sciences Mathématiques 1 Journal of High Energy Physics 1 Qualitative Theory of Dynamical Systems 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Communications on Pure and Applied Analysis 1 Journal of Applied Mathematics and Computing 1 International Journal of Number Theory 1 Complex Variables and Elliptic Equations 1 Proceedings of the Steklov Institute of Mathematics 1 Journal of Fixed Point Theory and Applications 1 Complex Analysis and Operator Theory 1 Journal of Noncommutative Geometry 1 Acta Mathematica Universitatis Ostraviensis 1 International Journal of Differential Equations 1 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 1 Philosophical Transactions A. Royal Society of London
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#### Cited in 40 Fields

 65 Measure and integration (28-XX) 61 Number theory (11-XX) 17 Functional analysis (46-XX) 16 Probability theory and stochastic processes (60-XX) 15 Dynamical systems and ergodic theory (37-XX) 14 Quantum theory (81-XX) 13 Functions of a complex variable (30-XX) 11 Partial differential equations (35-XX) 9 Operator theory (47-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 7 Algebraic geometry (14-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Convex and discrete geometry (52-XX) 5 Combinatorics (05-XX) 5 Group theory and generalizations (20-XX) 5 Ordinary differential equations (34-XX) 4 Special functions (33-XX) 3 Topological groups, Lie groups (22-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Geometry (51-XX) 3 Relativity and gravitational theory (83-XX) 2 General and overarching topics; collections (00-XX) 2 Real functions (26-XX) 2 Potential theory (31-XX) 2 Abstract harmonic analysis (43-XX) 2 Differential geometry (53-XX) 2 General topology (54-XX) 2 Computer science (68-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX)

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