Research Victor Beresnevich
University of York

Interests Publications Projects Events/Visitors Other

Preprints :

Inhomogeneous theory of dual Diophantine approximation on manifolds
(with Dzmitry Badziahin, and Sanju Velani, 37 pages, 28 Sep 2010 )
arXiv:1009.5638
Full text: pdf(348KB) ps(585KB) dvi(147KB)

Rational points near manifolds and metric Diophantine approximation
(46 pages, updated 03 June 2009),
arXiv:0904.0474
Full text: pdf(411KB) ps(949KB) dvi(440KB)

Simultaneous inhomogeneous Diophantine approximation on manifolds
(with Sanju Velani, 13 pages, Jul 2007, Dedicated to A.O. Gelfond on what would have been his 100th birthday),
Proceeding of the conference 'Diophantine and Analytical Problems in Number Theory' Moscow State University, 2007 (to appear)
arXiv:0710.5685
Full text: pdf(214KB) ps(234KB) dvi(58KB)

In Press :

Inhomogeneous Diophantine approximation on planar curves
(with Sanju Velani, and Robert C. Vaughan, 11 pages, 16 Mar 2009),
Math. Ann. To appear.
arXiv:0903.2817
Full text: pdf(186KB) ps(220KB) dvi(48KB)

An Inhomogeneous Transference Principle and Diophantine Approximation
(with Sanju Velani, 37 pages, 28 Feb 2008),
Proc. Lond. Math. Soc. To appear.
arXiv:0802.1837
Full text: pdf(422KB) ps(421KB) dvi(175KB)

On the distribution of values of discriminants of integral polynomials
(with Vasili Bernik and Friedrich Goetze, 4 pages, In Russian, updated 20 April 2010),
Dokl. Nats. Akad. Nauk Belarusi. To appear.
Full text: pdf(165KB) ps(292KB) dvi(22KB)

2010 :

Explicit bounds for rational points near planar curves and metric Diophantine approximation
(with Evgeniy Zorin, 24 pages, 20 April 2010),
Adv. Math. 225 (2010), 3064-3087.
arXiv:1002.2803
Full text: pdf(295KB) ps(514KB) dvi(119KB)

The distribution of close conjugate algebraic numbers
(with Vasili Bernik and Friedrich Goetze, 16 pages, 30 June 2009),
Compositio Mathematica. 146 (2010), 1165-1179.
arXiv:0906.4286
Full text: pdf(271KB) ps(538KB) dvi(144KB)

Classical metric Diophantine approximation revisited: the Khintchine-Groshev theorem
(with Sanju Velani)
Int. Math. Res. Not. (2010), no. 1, 69-86.
arXiv:0811.0809
Full text: pdf(221KB) ps(371KB) dvi(66KB)

2009 :

Ubiquity and a general logarithm law for geodesics
(with Sanju Velani),
Bugeaud, Y. (ed.) et al. Dynamical Systems and Diophantine Approximation. Seminaires et Congres 20 (2009), 21-36.
arXiv:0707.1225
Full text: pdf(220KB) ps(252KB) dvi(66KB)

Classical metric Diophantine approximation revisited
(with Vasilii Bernik, Maurice Dodson and Sanju Velani),
Chen, W. W. L. (ed.) et al., Analytic number theory. Essays in honour of Klaus Roth on the occasion of his 80th birthday. Cambridge: Cambridge University Press. (2009), 38-61.
Full text: pdf(319KB) ps(356KB) dvi(124KB)

2008 :

A note on zero-one laws in metrical Diophantine approximation
(with Sanju Velani),
Acta Arith. 133 (2008), no. 4, 363-374.
Full text: pdf(215KB) ps(229KB) dvi(54KB)

An inhomogeneous wave equation and non-linear Diophantine approximation
(with Simon Kristensen, Maurice Dodson, Jason Levesley),
Adv. Math. 217 (2008), no. 2, 740-760.
Full text: pdf(245KB) ps(339KB)

2007 :

A note on simultaneous Diophantine approximation on planar curves
(with Sanju Velani),
Math. Ann. 337 (2007), 769-796.
Full text: pdf(273KB) ps(334KB) dvi(100KB)

Diophantine approximation on planar curves and the distribution of rational points (with an appendix by R.C. Vaughan: Sums of two squares near perfect squares)
(with Detta Dickinson and Sanju Velani),
Ann. of Math. (2) 166 (2007), 367426.
Full text: pdf(420KB) ps(635KB) dvi(250KB)

2006 :

Schmidt's theorem, Hausdorff measures and Slicing
(with Sanju Velani),
Int. Math. Res. Notices, Article ID 48794, 2006, 24 pages.
Full text: pdf(255KB) ps(301KB) dvi(80KB)

A Mass Transference Principle and the Duffin-Schaeffer conjecture for Hausdorff measures
(with Sanju Velani),
Ann. of Math. (2) 164 (2006), no. 3, 971-992.
http://annals.math.princeton.edu/issues/2006/Nov2006/
Full text: pdf(437KB) ps(304KB) dvi(86KB)

Measure theoretic laws for lim sup sets
(with Detta Dickinson and Sanju Velani),
Memoirs of the AMS 179 (2006), no. 846, 91 pages.
Full text: pdf(565KB) ps(742KB) dvi(347KB)

2005 :

On a theorem of V.Bernik in the metrical theory of Diophantine approximation
Acta Arith., 117 (2005), no. 1, 71-80.
Full text: pdf(186KB) ps(202KB) dvi(42KB)

On approximation of p-adic numbers by p-adic algebraic numbers
(with V. I. Bernik and E. I. Kovalevskaya),
J. Number Theory, 111 (2005), no. 1, 33-56.
Full text: pdf(254KB) ps(306KB) dvi(86KB)

2003 :

On the construction of regular systems of points with real, complex, and p-adic algebraic coordinates
Vestsi Nats. Akad. Navuk Belarusi Ser. Fi z.-Mat. Navuk, no.1 (2003), 22-27 (in Russian).
Full text: pdf(244KB) ps(228KB) dvi(48KB)

On Diophantine approximations of dependent quantities in the p-adic case
(with E. I. Kovalevskaya),
Mat. Zametki, 73 (2003), no. 1, 22-37. (in Russian)
Full text: pdf(294KB) ps(324KB) dvi(89KB)

On generation of prime numbers
(with D. V. Vasilyev),
Vestsi Nats. Akad. Navuk Belarusi Ser. Fi z.-Mat. Navuk, (2003), no. 2, 5-10. (in Russian)
Full text: pdf(193KB) ps(171KB) dvi(36KB)

2002 :

A Groshev type theorem for convergence on manifolds
Acta Math. Hungar, 94 (2002), 99-130.
Full text: pdf(301KB) ps(658KB) dvi(136KB)

Diophantine approximation on classical curves and Hausdorff dimension
(with V. I. Bernik),
Conference Proceedings: Analytic and probabilistic methods in number theory (Palanga, 2001). (2002) 20-27, Publisher: TEV, Vilnius.
Full text: pdf(179KB) ps(182KB) dvi(37KB)

Metric Diophantine approximation: the Khintchine-Groshev theorem for non-degenerate manifolds
(with V. I. Bernik, D. Y. Kleinbock and G. A. Margulis),
Mosc. Math. J., 2 (2002), no. 2, 203-225.
Full text: pdf(424KB)

Metric theorems on the approximation of p-adic numbers by algebraic numbers of bounded degree
(with V. I. Bernik and E. I. Kovalevskaya),
Dokl. Nats. Akad. Nauk Belarusi, 46 (2002), no. 4, 13-15. (in Russian)
Full text: pdf(208KB)

On the Hausdorff dimension of sets of well approximable points on non-degenerate curves
(with V. I. Bernik and M.M. Dodson),
Dokl. Nats. Akad. Nauk Belarusi, 46 (2002), no. 6, 18-20. (in Russian)
Full text: pdf(214KB)

Regular systems, ubiquity and Diophantine approximation
(with V. I. Bernik and M.M. Dodson),
A panorama of number theory or the view from Baker's garden (Zurich, 1999) (2002) 260-279, Publisher: CUP.
Full text: pdf(152KB)

2001 :

An analogue of the Khintchine theorem for curves in a three-dimensional complex space
(with D. V. Vasilyev),
Vestsi Nats. Akad. Navuk Belarusi Ser. Fi z.-Mat. Navuk, (2001), no. 1, 5-7. (in Russian)
Full text: pdf(200KB) ps(168KB) dvi(24KB)

Sets of exact 'logarithmic' order in the theory of Diophantine approximation
(with Detta Dickinson and Sanju Velani),
Math Annalen, 321 (2001) 253-273.
Full text: pdf(196KB) ps(239KB) dvi(94KB)

The distribution of rational points near a parabola
Dokl. Nats. Akad. Nauk Belarusi, 45 (2001), no. 2, 21-23. (in Russian)
Full text: pdf(205KB)

2000 :

A. Baker's conjecture and Hausdorff dimension
(with V. I. Bernik),
Publ. Math. Debrecen, 56 (2000), no. 3-4, 263-269.
Full text: pdf(137KB) ps(139KB) dvi(24KB)

An analogue of the Khinchin-Groshev theorem for nondegenerate manifolds in R^n
Dokl. Nats. Akad. Nauk Belarusi, 44 (2000), no. 4, 42-45. (in Russian)
Full text: pdf(225KB)

An analogue of the Khinchin-Groshev theorem for curves in R^n
Dokl. Nats. Akad. Nauk Belarusi, 44 (2000), no. 3, 29-32. (in Russian)
Full text: pdf(233KB)

On proving analogues of the Khintchine theorem for curves
Vestsi Nats. Akad. Navuk Belarusi. Ser. Fiz.-Mat., (2000), no. 3, 35-40. (in Russian)
Full text: pdf(264KB) ps(237KB) dvi(50KB)

Application of the concept of regular systems of points in metric number theory
Vestsi Nats. Akad. Navuk Belarusi. Ser. Fiz.-Mat., (2000), no. 1, 35-39. (in Russian)
Full text: pdf(205KB) ps(180KB) dvi(33KB)

On linear manifolds for which the Khintchine approximation theorem holds
(with V. I. Bernik, H. Dickinson and M.M. Dodson)
Vestsi Nats. Akad. Navuk Belarusi. Ser. Fiz.-Mat., (2000), no. 2, 14-17. (in Byelorussian)
Full text: pdf(229KB) ps(178KB) dvi(29KB)

Regular systems and linear Diophantine approximations on manifolds
Dokl. Nats. Akad. Nauk Belarusi, 44 (2000), no. 5, 37-39. (in Russian)
Full text: pdf(219KB)

1999 :

A multipoint problem with multiple knots for linear hyperbolic equations
(with V. I. Bernik, P. B. Vasilishin and B. I. Ptashnik)
Ukrain. Mat. Zh., 51 (1999), no. 10, 1311-1316. (in Ukrainian)

An analogue of Khintchine's theorem for simultaneous approximation of points on curves in R3
Tr. Inst. Mat. (Minsk), 3 (1999), 3-9. Publisher: Inst. Math., Minsk. (in Russian)
Full text: pdf(262KB) ps(264KB) dvi(64KB)

Best order of approximation of points of smooth curves in a three-dimensional Euclidean space
Dokl. Nats. Akad. Nauk Belarusi, 43 (1999), no. 4, 9-13. (in Russian)
Full text: pdf(224KB) ps(193KB) dvi(32KB)

Exact order of approximation of real numbers by algebraic numbers
Dokl. Akad. Nauk, 366 (1999), no. 5, 583-586. (in Russian)
Full text: pdf(186KB) ps(193KB) dvi(34KB)

On approximation of real numbers by real algebraic numbers
Acta Arith., 90 (1999), no. 2, 97-112.
Full text: pdf(178KB) ps(230KB) dvi(76KB)

The Khintchine-Groshev theorem for planar curves
(with V. I. Bernik, H. Dickinson and M.M. Dodson)
Proc. Roy. Soc. Lond A, 455 (1999), 3053-3063.
Full text: pdf(328KB)

1997 :

Inhomogeneous non-linear Diophantine approximation
(with V.I. Bernik and M.M. Dodson)
Proceedings of the conference : `Diophantine analysis and its applications', in honour of Sprindzuk (1997), 13-20. Publisher: Inst. Math., Minsk.
Full text: pdf(152KB) ps(188KB) dvi(50KB)

The distribution of zeros of smooth functions with three degrees of freedom
Proceedings of the conference : `Diophantine analysis and its applications', in honour of Sprindzuk (1997), 7-12. Publisher: Inst. Math., Minsk. (in Russian)
Full text: pdf(201KB) ps(198KB) dvi(46KB)

1996 :

Effective estimates for measures of sets of real numbers with a given order of approximation by quadratic irrationalities
Vestsi Akad. Navuk Belarusi Ser. Fiz.-Mat. Navuk (1996), no. 4, 10-15. (in Russian)
Full text: pdf(211KB) ps(210KB) dvi(46KB)

On a metrical theorem of W. Schmidt
(with V. I. Bernik)
Acta Arith. 75 (1996), no. 3, 219-233.
Full text: pdf(189KB) ps(221KB) dvi(70KB)

On the dependence of orders of approximations of points of plane curves and the vector of derivatives
Vestsi Akad. Navuk Belarusi Ser. Fi z.-Mat. Navuk (1996), no. 3, 125-129. (in Russian)
Full text: pdf(143KB) ps(147KB) dvi(32KB)

1994 :

Extremal smooth curves in three-dimensional Euclidean space
(with V. I. Bernik)
Dokl. Akad. Nauk Belarusi 38 (1994), no. 3, 9-12. (in Russian)

Simultaneous approximations of zero by values of smooth functions
Vestsi Akad. Navuk Belarusi Ser. Fiz. Mat. Navuk (1994), no. 3, 20-25. (in Russian)