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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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On the cubic $L$-function
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by N. V. Proskurin
Translated by: A. Plotkin
St. Petersburg Math. J. 24 (2013), 353-370
DOI: https://doi.org/10.1090/S1061-0022-2013-01242-8
Published electronically: January 22, 2013
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Abstract:

The cubic $L$-function is related to the cubic Kubota–Patterson theta function via the Mellin transformation. The cubic $L$-function obeys a functional equation of the Riemann type (with two gamma factors), but admits no expansion in an Euler product. In the paper, the cubic $L$-function is studied, and the distribution problem for the real parts of its zeros is considered. Some conjectures based on calculations are stated.
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Bibliographic Information
  • N. V. Proskurin
  • Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences Fontanka 27, Saint Petersburg 191023, Russia
  • Email: np@pdmi.ras.ru
  • Received by editor(s): March 11, 2011
  • Published electronically: January 22, 2013
  • Additional Notes: The author was supported by RFBR (grant no. 11-01-00239-a)
  • © Copyright 2013 American Mathematical Society
  • Journal: St. Petersburg Math. J. 24 (2013), 353-370
  • MSC (2010): Primary 11F27
  • DOI: https://doi.org/10.1090/S1061-0022-2013-01242-8
  • MathSciNet review: 3013333