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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Average number of local minima for three-dimensional integral lattices
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by A. A. Illarionov
Translated by: S. Kislyakov
St. Petersburg Math. J. 23 (2012), 551-570
DOI: https://doi.org/10.1090/S1061-0022-2012-01208-2
Published electronically: March 2, 2012
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Abstract:

An asymptotic formula is found for the average number of local minima of three-dimensional complete integral lattices with determinant in the interval $[1,N]$. This is a generalization to the two-dimensional case of the classical result about the average length of a finite continued fraction with denominator belonging to $[1,N]$.
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Bibliographic Information
  • A. A. Illarionov
  • Affiliation: Khabarovsk Division, Institute of Applied Mathematics, Russian Academy of Sciences, 54 Dzerzhinskiǐ Street, Khabarovsk 680000, Russia
  • Received by editor(s): November 30, 2009
  • Published electronically: March 2, 2012
  • Additional Notes: Supported by RFBR (grants nos. 10-01-98002r-siberia-a , 11-01-00628-a), by FED RAS (grants nos. 11-III-V-01M-002, 09-I-114-03), and by the grant MD-2339.2010.1 of the President of RF
  • © Copyright 2012 American Mathematical Society
  • Journal: St. Petersburg Math. J. 23 (2012), 551-570
  • MSC (2010): Primary 11H06
  • DOI: https://doi.org/10.1090/S1061-0022-2012-01208-2
  • MathSciNet review: 2896168