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`

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**Rational points near manifolds and metric Diophantine approximation**

(`46 pages, updated 03 June 2009`),

* * `arXiv:0904.0474`

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**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)

In Press :

**Inhomogeneous Diophantine approximation on planar curves**

(with *Sanju Velani, and Robert C. Vaughan*, `11 pages, 16 Mar 2009`),

** Math. Ann. ** To appear.

**An Inhomogeneous Transference Principle and Diophantine Approximation**

(with *Sanju Velani*, `37 pages, 28 Feb 2008`),

** Proc. Lond. Math. Soc. ** To appear.

**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.

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.

**The distribution of close conjugate algebraic numbers**

(with *Vasili Bernik and Friedrich Goetze*, `16 pages, 30 June 2009`),

** Compositio Mathematica. 146 ** (2010), 1165-1179.

**Classical metric Diophantine approximation revisited: the Khintchine-Groshev theorem**

(with *Sanju Velani*)

** Int. Math. Res. Not. ** (2010), no. 1, 69-86.

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.

**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.

2008 :

**A note on zero-one laws in metrical Diophantine approximation**

(with *Sanju Velani)*,

** Acta Arith. 133** (2008), no. 4, 363-374.

**An inhomogeneous wave equation and non-linear Diophantine approximation**

(with *Simon Kristensen, Maurice Dodson, Jason Levesley*),

** Adv. Math. 217** (2008), no. 2, 740-760.

2007 :

**A note on simultaneous Diophantine approximation on planar curves**

(with *Sanju Velani*),

*Math. Ann.*** 337** (2007), 769-796.

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**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), 367–426.

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2006 :

**Schmidt's theorem, Hausdorff measures and Slicing**

(with *Sanju Velani*),

** Int. Math. Res. Notices,** Article ID 48794, 2006, 24 pages.

**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/`

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**Measure theoretic laws for lim sup sets**

(with *Detta Dickinson and Sanju Velani*),

*Memoirs of the AMS*** 179 ** (2006), no. 846, 91 pages.

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2005 :

**On a theorem of V.Bernik in the metrical theory of Diophantine approximation**

*Acta Arith.,***117** (2005), no. 1, 71-80.

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**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.

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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).

**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)

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**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)

2002 :

**A Groshev type theorem for convergence on manifolds**

*Acta Math. Hungar,***94** (2002), 99-130.

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**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.

**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.

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**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)

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**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)

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**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.

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)

**Sets of exact 'logarithmic' order in the theory of Diophantine approximation**

(with *Detta Dickinson and Sanju Velani*),

*Math Annalen,***321** (2001) 253-273.

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**The distribution of rational points near a parabola**

*Dokl. Nats. Akad. Nauk Belarusi,***45** (2001), no. 2, 21-23. (in Russian)

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2000 :

**A. Baker's conjecture and Hausdorff dimension**

(with *V. I. Bernik*),

*Publ. Math. Debrecen,***56** (2000), no. 3-4, 263-269.

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**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)

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**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)

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**On proving analogues of the Khintchine theorem for curves**

** Vestsi Nats. Akad. Navuk Belarusi. Ser. Fiz.-Mat.,** (2000), no. 3, 35-40. (in Russian)

**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)

**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)

**Regular systems and linear Diophantine approximations on manifolds**

*Dokl. Nats. Akad. Nauk Belarusi,***44** (2000), no. 5, 37-39. (in Russian)

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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)

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**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)

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**Exact order of approximation of real numbers by algebraic numbers**

*Dokl. Akad. Nauk,***366** (1999), no. 5, 583-586. (in Russian)

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**On approximation of real numbers by real algebraic numbers**

*Acta Arith.,***90** (1999), no. 2, 97-112.

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**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.

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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.

**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)

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)

**On a metrical theorem of W. Schmidt**

(with *V. I. Bernik*)

*Acta Arith.***75** (1996), no. 3, 219-233.

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**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)

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)