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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

On the cubic $ L$-function


Author: N. V. Proskurin
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 24 (2012), nomer 2.
Journal: St. Petersburg Math. J. 24 (2013), 353-370
MSC (2010): Primary 11F27
Published electronically: January 22, 2013
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Abstract | References | Similar Articles | Additional Information

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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Additional 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

DOI: http://dx.doi.org/10.1090/S1061-0022-2013-01242-8
PII: S 1061-0022(2013)01242-8
Keywords: Cubic $L$-function, distribution of zeros
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)
Article copyright: © Copyright 2013 American Mathematical Society