Kleinbock, Dmitry; Skenderi, Mishel Khintchine-type theorems for values of subhomogeneous functions at integer points. (English) Zbl 07328625 Monatsh. Math. 194, No. 3, 523-554 (2021). MSC: 11D75 11J54 11J83 11H06 PDF BibTeX XML Cite \textit{D. Kleinbock} and \textit{M. Skenderi}, Monatsh. Math. 194, No. 3, 523--554 (2021; Zbl 07328625) Full Text: DOI
Bandi, Prasuna; Ghosh, Anish; Han, Jiyoung A generic effective Oppenheim theorem for systems of forms. (English) Zbl 07257232 J. Number Theory 218, 311-333 (2021). MSC: 11H60 11H55 11K60 PDF BibTeX XML Cite \textit{P. Bandi} et al., J. Number Theory 218, 311--333 (2021; Zbl 07257232) Full Text: DOI
Prasad, Dipendra Contributions to algebraic number theory from India : from independence to late 90’s. (English) Zbl 1431.11002 Indian J. Pure Appl. Math. 50, No. 3, 779-793 (2019). MSC: 11-02 11-03 11Rxx PDF BibTeX XML Cite \textit{D. Prasad}, Indian J. Pure Appl. Math. 50, No. 3, 779--793 (2019; Zbl 1431.11002) Full Text: DOI
Athreya, Jayadev S.; Margulis, Gregory A. Values of random polynomials at integer points. (English) Zbl 1454.11126 J. Mod. Dyn. 12, 9-16 (2018). Reviewer: Symon Serbenyuk (Kyïv) MSC: 11H60 11P21 11C08 PDF BibTeX XML Cite \textit{J. S. Athreya} and \textit{G. A. Margulis}, J. Mod. Dyn. 12, 9--16 (2018; Zbl 1454.11126) Full Text: DOI
Han, Jiyoung; Lim, Seonhee; Mallahi-Karai, Keivan Asymptotic distribution of values of isotropic here quadratic forms at \(S\)-integral points. (English) Zbl 1407.11084 J. Mod. Dyn. 11, 501-550 (2017). MSC: 11H50 22E40 22D40 11P21 05C15 37E25 68R15 PDF BibTeX XML Cite \textit{J. Han} et al., J. Mod. Dyn. 11, 501--550 (2017; Zbl 1407.11084) Full Text: DOI
Bourgain, Jean A quantitative Oppenheim theorem for generic diagonal quadratic forms. (English) Zbl 1361.11024 Isr. J. Math. 215, No. 1, 503-512 (2016). Reviewer: Meinhard Peters (Münster) MSC: 11E20 11L07 PDF BibTeX XML Cite \textit{J. Bourgain}, Isr. J. Math. 215, No. 1, 503--512 (2016; Zbl 1361.11024) Full Text: DOI arXiv
Witte Morris, Dave Dani’s work on dynamical systems on homogeneous spaces. (English) Zbl 1332.37005 Bhattacharya, Siddhartha (ed.) et al., Recent trends in ergodic theory and dynamical systems. International conference in honor of S. G. Dani’s 65th birthday, Vadodara, India, December 26–29, 2012. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-0931-9/pbk; 978-1-4704-2219-6/ebook). Contemporary Mathematics 631, 131-144 (2015). MSC: 37A17 37-02 37D40 11H55 37A45 PDF BibTeX XML Cite \textit{D. Witte Morris}, Contemp. Math. 631, 131--144 (2015; Zbl 1332.37005) Full Text: arXiv
Kleinbock, Dmitry; Weiss, Barak Values of binary quadratic forms at integer points and Schmidt games. (English) Zbl 1332.37004 Bhattacharya, Siddhartha (ed.) et al., Recent trends in ergodic theory and dynamical systems. International conference in honor of S. G. Dani’s 65th birthday, Vadodara, India, December 26–29, 2012. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-0931-9/pbk; 978-1-4704-2219-6/ebook). Contemporary Mathematics 631, 77-92 (2015). MSC: 37A17 37N40 37D40 11J06 11J83 PDF BibTeX XML Cite \textit{D. Kleinbock} and \textit{B. Weiss}, Contemp. Math. 631, 77--92 (2015; Zbl 1332.37004) Full Text: arXiv
Lindenstrauss, Elon; Margulis, Gregory Effective estimates on indefinite ternary forms. (English) Zbl 1308.37002 Isr. J. Math. 203, 445-499 (2014). Reviewer: Jean Raimbault (Toulouse) MSC: 37A17 22E40 22F30 11E25 PDF BibTeX XML Cite \textit{E. Lindenstrauss} and \textit{G. Margulis}, Isr. J. Math. 203, 445--499 (2014; Zbl 1308.37002) Full Text: DOI
Margulis, Gregory; Mohammadi, Amir Quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms. (English) Zbl 1243.11054 Duke Math. J. 158, No. 1, 121-160 (2011). Reviewer: Ranjeet Sehmi (Chandigarh) MSC: 11E20 58J50 PDF BibTeX XML Cite \textit{G. Margulis} and \textit{A. Mohammadi}, Duke Math. J. 158, No. 1, 121--160 (2011; Zbl 1243.11054) Full Text: DOI
Venkatesh, Akshay The work of Einsiedler, Katok and Lindenstrauss on the Littlewood conjecture. (English) Zbl 1194.11075 Bull. Am. Math. Soc., New Ser. 45, No. 1, 117-134 (2008). Reviewer: Ranjeet Sehmi (Chandigarh) MSC: 11J13 37A35 11H46 37A45 PDF BibTeX XML Cite \textit{A. Venkatesh}, Bull. Am. Math. Soc., New Ser. 45, No. 1, 117--134 (2008; Zbl 1194.11075) Full Text: DOI
German, O. N.; Lakshtanov, E. L. On a multidimensional generalization of Lagrange’s theorem on continued fractions. (English. Russian original) Zbl 1180.11022 Izv. Math. 72, No. 1, 47-61 (2008); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 1, 51-66 (2008). Reviewer: Iskander Aliev (Cardiff) MSC: 11H06 11H46 11H50 PDF BibTeX XML Cite \textit{O. N. German} and \textit{E. L. Lakshtanov}, Izv. Math. 72, No. 1, 47--61 (2008; Zbl 1180.11022); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 1, 51--66 (2008) Full Text: DOI
Dani, S. G. Diophantine approximation and dynamics of unipotent flows on homogeneous spaces. (English) Zbl 1151.11032 Pure Appl. Math. Q. 4, No. 1, 147-166 (2008). Reviewer: Simon Kristensen (Aarhus) MSC: 11J25 11J83 22E40 37A17 37A45 PDF BibTeX XML Cite \textit{S. G. Dani}, Pure Appl. Math. Q. 4, No. 1, 147--166 (2008; Zbl 1151.11032) Full Text: DOI
Müller, Wolfgang Systems of quadratic Diophantine inequalities and the value distribution of quadratic forms. (English) Zbl 1184.11011 Monatsh. Math. 153, No. 3, 233-250 (2008). Reviewer: Koichi Kawada (Morioka) MSC: 11D75 11J25 PDF BibTeX XML Cite \textit{W. Müller}, Monatsh. Math. 153, No. 3, 233--250 (2008; Zbl 1184.11011) Full Text: DOI
Elsner, Guido Distributions of values of indefinite forms and higher-order spectral estimates for finite Markov chains. (English) Zbl 1206.11123 Bielefeld: Univ. Bielefeld, Fakultät für Mathematik (Diss.). 74 p. (2006). Reviewer: Guido Elsner MSC: 11P21 37A30 60J10 11H50 PDF BibTeX XML Cite \textit{G. Elsner}, Distributions of values of indefinite forms and higher-order spectral estimates for finite Markov chains. Bielefeld: Univ. Bielefeld, Fakultät für Mathematik (Diss.) (2006; Zbl 1206.11123)
Margulis, Gregory Diophantine approximation, lattices and flows on homogeneous spaces. (English) Zbl 1036.11033 Wüstholz, Gisbert (ed.), A panorama in number theory or The view from Baker’s garden. Based on a conference in honor of Alan Baker’s 60th birthday, Zürich, Switzerland, 1999. Cambridge: Cambridge University Press (ISBN 0-521-80799-9/hbk). 280-310 (2002). Reviewer: Ranjeet Sehmi (Chandigarh) MSC: 11J83 22E40 11E57 PDF BibTeX XML Cite \textit{G. Margulis}, in: A panorama in number theory or The view from Baker's garden. Based on a conference in honor of Alan Baker's 60th birthday, Zurich, Switzerland, 1999. Cambridge: Cambridge University Press. 280--310 (2002; Zbl 1036.11033)
Zhan, Xingzhi Matrix inequalities. (English) Zbl 1018.15016 Lecture Notes in Mathematics. 1790. Berlin: Springer. vii, 116 p. EUR 22.95/net; sFr. 39.50; £16.00; $ 29.80 (2002). Reviewer: Arnold Richard Kräuter (Leoben) MSC: 15A45 15-02 15A15 15A18 15A42 15A60 15B48 26D15 15B51 PDF BibTeX XML Cite \textit{X. Zhan}, Matrix inequalities. Berlin: Springer (2002; Zbl 1018.15016) Full Text: DOI Link
Marklof, Jens The Berry-Tabor conjecture. (English) Zbl 1023.81011 Casacuberta, Carles (ed.) et al., 3rd European congress of mathematics (ECM), Barcelona, Spain, July 10-14, 2000. Volume II. Basel: Birkhäuser. Prog. Math. 202, 421-427 (2001). MSC: 81Q50 81-02 11H50 PDF BibTeX XML Cite \textit{J. Marklof}, Prog. Math. 202, 421--427 (2001; Zbl 1023.81011)
Dani, Shrikrishna G. On the Oppenheim conjecture on values of quadratic forms. (English) Zbl 1011.11046 Ghys, Étienne (ed.) et al., Essays on geometry and related topics. Mémoires dédiés à André Haefliger. Vol. 1. Genève: L’Enseignement Mathématique. Monogr. Enseign. Math. 38, 257-270 (2001). Reviewer: Ranjeet Sehmi (Chandigarh) MSC: 11H50 PDF BibTeX XML Cite \textit{S. G. Dani}, Monogr. Enseign. Math. 38, 257--270 (2001; Zbl 1011.11046)
Dani, S. G. On values of linear and quadratic forms at integral points. (English) Zbl 0986.11044 Bambah, R. P. (ed.) et al., Number theory. Basel: Birkhäuser. Trends in Mathematics. 107-119 (2000). Reviewer: Ranjeet Sehmi (Chandigarh) MSC: 11H50 22E40 22F30 PDF BibTeX XML Cite \textit{S. G. Dani}, in: Number theory. Basel: Birkhäuser. 107--119 (2000; Zbl 0986.11044)
Bekka, M. Bachir; Mayer, Matthias Ergodic theory and topological dynamics of group actions on homogeneous spaces. (English) Zbl 0961.37001 London Mathematical Society Lecture Note Series. 269. Cambridge: Cambridge University Press. x, 200 p. (2000). Reviewer: Tomasz Downarowicz (Wrocław) MSC: 37-02 37B05 37D40 22F30 11H55 37A17 37A25 37A15 37A45 37Axx 57S20 37C85 PDF BibTeX XML Cite \textit{M. B. Bekka} and \textit{M. Mayer}, Ergodic theory and topological dynamics of group actions on homogeneous spaces. Cambridge: Cambridge University Press (2000; Zbl 0961.37001)
Witte, Dave; Yukie, Akihiko; Zierau, Roger Prehomogeneous vector spaces and ergodic theory. II. (English) Zbl 0994.11040 Trans. Am. Math. Soc. 352, No. 4, 1687-1708 (2000). Reviewer: Ranjeet Sehmi (Chandigarh) MSC: 11S90 22E40 22D40 11H50 PDF BibTeX XML Cite \textit{D. Witte} et al., Trans. Am. Math. Soc. 352, No. 4, 1687--1708 (2000; Zbl 0994.11040) Full Text: DOI arXiv
Bentkus, V.; Götze, F. Lattice point problems and distribution of values of quadratic forms. (English) Zbl 0979.11048 Ann. Math. (2) 150, No. 3, 977-1027 (1999). Reviewer: Ekkehard Krätzel (Wien) MSC: 11P21 PDF BibTeX XML Cite \textit{V. Bentkus} and \textit{F. Götze}, Ann. Math. (2) 150, No. 3, 977--1027 (1999; Zbl 0979.11048) Full Text: DOI Link EuDML
Eskin, Alex; Margulis, Gregory; Mozes, Shahar Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture. (English) Zbl 0906.11035 Ann. Math. (2) 147, No. 1, 93-141 (1998). Reviewer: R.Sehmi (Chandigarh) MSC: 11H50 22E40 22D40 11P21 PDF BibTeX XML Cite \textit{A. Eskin} et al., Ann. Math. (2) 147, No. 1, 93--141 (1998; Zbl 0906.11035) Full Text: DOI
Eskin, Alex Counting problems and semisimple groups. (English) Zbl 0901.11029 Doc. Math., Extra Vol. ICM Berlin 1998, vol. II, 539-552 (1998). Reviewer: B.Z.Moroz (Bonn) MSC: 11P21 22E40 11J25 11H50 22D40 81Q50 PDF BibTeX XML Cite \textit{A. Eskin}, Doc. Math. Extra Vol., 539--552 (1998; Zbl 0901.11029) Full Text: EMIS EuDML
Sarnak, Peter Values at integers of binary quadratic forms. (English) Zbl 0911.11032 Drury, S. W. (ed.) et al., Harmonic analysis and number theory. Papers in honour of Carl S. Herz. Proceedings of the conference, April 15–19, 1996, Montréal, Canada. Providence, RI: American Mathematical Society. CMS Conf. Proc. 21, 181-203 (1997). Reviewer: R.Sehmi (Chandigarh) MSC: 11H55 11G99 37-XX 11E16 PDF BibTeX XML Cite \textit{P. Sarnak}, in: Harmonic analysis and number theory. Papers in honour of Carl S. Herz. Proceedings of the conference, April 15--19, 1996, Montréal, Canada. Providence, RI: American Mathematical Society. 181--203 (1997; Zbl 0911.11032)
Yukie, Akihiko Prehomogeneous vector spaces and ergodic theory. I. (English) Zbl 0896.11013 Duke Math. J. 90, No. 1, 123-147 (1997). Reviewer: Ranjeet Sehmi (Chandigarh) MSC: 11E04 11S90 28D20 11H55 14M17 17B20 PDF BibTeX XML Cite \textit{A. Yukie}, Duke Math. J. 90, No. 1, 123--147 (1997; Zbl 0896.11013) Full Text: DOI arXiv
Dani, S. G. Studying values of quadratic forms through dynamics. (English) Zbl 0882.11041 Adhikari, S. D. (ed.), Current trends in mathematics and physics. A tribute to Harish-Chandra. New Delhi: Narosa Publishing House. 45-52 (1995). Reviewer: R.Sehmi (Chandigarh) MSC: 11H50 28D99 22E40 PDF BibTeX XML Cite \textit{S. G. Dani}, in: Current trends in mathematics and physics. A tribute to Harish-Chandra. New Delhi: Narosa Publishing House. 45--52 (1995; Zbl 0882.11041)
Eskin, Alex; Margulis, Gregory; Mozes, Shahar On a quantitative version of the Oppenheim conjecture. (English) Zbl 0859.11043 Electron. Res. Announc. Am. Math. Soc. 1, No. 3, 124-130 (1995). Reviewer: R.Sehmi (Chandigarh) MSC: 11H50 11J25 22E40 PDF BibTeX XML Cite \textit{A. Eskin} et al., Electron. Res. Announc. Am. Math. Soc. 1, No. 3, 124--130 (1995; Zbl 0859.11043) Full Text: DOI EuDML
Borel, Armand Values of indefinite quadratic forms at integral points and flows on spaces of lattices. (English) Zbl 0852.22008 Bull. Am. Math. Soc., New Ser. 32, No. 2, 184-204 (1995). Reviewer: A.Borel (Princeton, NJ) MSC: 22E40 11H55 PDF BibTeX XML Cite \textit{A. Borel}, Bull. Am. Math. Soc., New Ser. 32, No. 2, 184--204 (1995; Zbl 0852.22008) Full Text: DOI arXiv
Ratner, Marina Interactions between ergodic theory, Lie groups, and number theory. (English) Zbl 0923.22002 Chatterji, S. D. (ed.), Proceedings of the international congress of mathematicians, ICM ’94, August 3-11, 1994, Zürich, Switzerland. Vol. I. Basel: Birkhäuser. 157-182 (1995). Reviewer: R.Sehmi (Chandigarh) MSC: 22D40 37D40 53D25 22E40 37A99 37C10 11F06 PDF BibTeX XML Cite \textit{M. Ratner}, in: Proceedings of the international congress of mathematicians, ICM '94, August 3-11, 1994, Zürich, Switzerland. Vol. I. Basel: Birkhäuser. 157--182 (1995; Zbl 0923.22002)
Dani, S. G. A proof of Margulis’ theorem on values of quadratic forms, independent of the axiom of choice. (English) Zbl 0816.11039 Enseign. Math., II. Sér. 40, No. 1-2, 49-58 (1994). Reviewer: R.Sehmi (Chandigarh) MSC: 11H55 PDF BibTeX XML Cite \textit{S. G. Dani}, Enseign. Math. (2) 40, No. 1--2, 49--58 (1994; Zbl 0816.11039)
Margulis, G. A.; Tomanov, G. M. Invariant measures for actions of unipotent groups over local fields on homogeneous spaces. (English) Zbl 0816.22004 Invent. Math. 116, No. 1-3, 347-392 (1994). Reviewer: H.Abels (Bielefeld) MSC: 22E40 28D15 11H55 20G25 22D40 PDF BibTeX XML Cite \textit{G. A. Margulis} and \textit{G. M. Tomanov}, Invent. Math. 116, No. 1--3, 347--392 (1994; Zbl 0816.22004) Full Text: DOI EuDML
Dani, S. G.; Margulis, G. A. Limit distributions of orbits of unipotent flows and values of quadratic forms. (English) Zbl 0814.22003 Gelfand, Sergej (ed.) et al., I. M. Gelfand Seminar. Part 1: Papers of the Gelfand seminar in functional analysis held at Moscow University, Russia, September 1993. Providence, RI: American Mathematical Society. Adv. Sov. Math. 16(1), 91-137 (1993). Reviewer: H.Abels (Bielefeld) MSC: 22E40 37C10 11H55 37A99 PDF BibTeX XML Cite \textit{S. G. Dani} and \textit{G. A. Margulis}, Adv. Sov. Math. 16, 91--137 (1993; Zbl 0814.22003)
Raghunathan, M. S. Values of quadratic forms. (English) Zbl 0770.11034 Indian J. Pure Appl. Math. 23, No. 5, 321-324 (1992). Reviewer: H.G.Quebbemann (Oldenburg) MSC: 11H50 11J25 PDF BibTeX XML Cite \textit{M. S. Raghunathan}, Indian J. Pure Appl. Math. 23, No. 5, 321--324 (1992; Zbl 0770.11034)
Rüschendorf, Ludger Fréchet-bounds and their applications. (English) Zbl 0744.60005 Advances in probability distributions with given marginals. Beyond the copulas, Lect. Symp., Rome/Italy, Math. Appl. 67, 151-187 (1991). Reviewer: J.Szulga (Auburn) MSC: 60A10 28A35 60C05 60B10 60E99 62B99 62H05 26D07 26B25 46A22 46A20 PDF BibTeX XML
Margulis, G. A. Lie groups and ergodic theory. (English) Zbl 0667.22005 Algebra: some current trends, Proc. 5th Natl. Sch. Algebra, Varna/Bulg. 1986, Lect. Notes Math. 1352, 130-146 (1988). Reviewer: S.G.Dani MSC: 22E40 37A99 43A85 11E16 11J99 PDF BibTeX XML
Kalpazidou, Sofia Khintchine’s constant for Lüroth representation. (English) Zbl 0647.10035 J. Number Theory 29, No. 2, 196-205 (1988). Reviewer: J.Galambos MSC: 11K16 PDF BibTeX XML Cite \textit{S. Kalpazidou}, J. Number Theory 29, No. 2, 196--205 (1988; Zbl 0647.10035) Full Text: DOI
Raka, Madhu On a conjecture of Watson. (English) Zbl 0517.10029 Math. Proc. Camb. Philos. Soc. 94, 9-22 (1983). Reviewer: E. Grosswald MSC: 11H50 PDF BibTeX XML Cite \textit{M. Raka}, Math. Proc. Camb. Philos. Soc. 94, 9--22 (1983; Zbl 0517.10029) Full Text: DOI