Limiting distribution of Frobenius numbers for n = 3

V. Shchur; Ya Sinai; A. Ustinov

doi:10.1016/j.jnt.2009.04.019

Limiting distribution of Frobenius numbers for n = 3

V. Shchur
, Ya Sinai
, A. Ustinov

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

The purpose of this paper is to give a complete derivation of the limiting distribution of large Frobenius numbers with three arguments outlined in the earlier work of J. Bourgain and Ya. Sinai and fill some gaps formulated there as hypotheses.

Original language	English (US)
Pages (from-to)	2778-2789
Number of pages	12
Journal	Journal of Number Theory
Volume	129
Issue number	11
DOIs	https://doi.org/10.1016/j.jnt.2009.04.019
State	Published - Nov 2009

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2009.04.019

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title = "Limiting distribution of Frobenius numbers for n = 3",

abstract = "The purpose of this paper is to give a complete derivation of the limiting distribution of large Frobenius numbers with three arguments outlined in the earlier work of J. Bourgain and Ya. Sinai and fill some gaps formulated there as hypotheses.",

author = "V. Shchur and Ya Sinai and A. Ustinov",

note = "Funding Information: The proof of the main theorem is given in Section 2. First we consider the sub-ensemble QN(0) and then explain how to extend the proof to QN. Recently J. Marklof using different methods proved the existence of the limiting distribution of 11 F (a) for any n (see [3]). N1+ n−1 The second author thanks NSF for the financial support, grant DMS No. 0600996. The research of the third author was supported by Russian Foundation for Basic Research (grant No. 07-01-00306), the Far Eastern Branch of the Russian Academy of Sciences (project No. 09-I-Π4-03), Dynasty Foundation and the Russian Science Support Foundation.",

year = "2009",

month = nov,

doi = "10.1016/j.jnt.2009.04.019",

language = "English (US)",

volume = "129",

pages = "2778--2789",

journal = "Journal of Number Theory",

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AU - Shchur, V.

AU - Sinai, Ya

AU - Ustinov, A.

N1 - Funding Information: The proof of the main theorem is given in Section 2. First we consider the sub-ensemble QN(0) and then explain how to extend the proof to QN. Recently J. Marklof using different methods proved the existence of the limiting distribution of 11 F (a) for any n (see [3]). N1+ n−1 The second author thanks NSF for the financial support, grant DMS No. 0600996. The research of the third author was supported by Russian Foundation for Basic Research (grant No. 07-01-00306), the Far Eastern Branch of the Russian Academy of Sciences (project No. 09-I-Π4-03), Dynasty Foundation and the Russian Science Support Foundation.

PY - 2009/11

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N2 - The purpose of this paper is to give a complete derivation of the limiting distribution of large Frobenius numbers with three arguments outlined in the earlier work of J. Bourgain and Ya. Sinai and fill some gaps formulated there as hypotheses.

AB - The purpose of this paper is to give a complete derivation of the limiting distribution of large Frobenius numbers with three arguments outlined in the earlier work of J. Bourgain and Ya. Sinai and fill some gaps formulated there as hypotheses.

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JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 11

ER -

Limiting distribution of Frobenius numbers for n = 3

Abstract

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