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On the zeros of the zeta function of the quadratic form $ x^2+y^2+z^2$


Author: N. V. Proskurin
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 27 (2015), nomer 2.
Journal: St. Petersburg Math. J. 27 (2016), 177-189
MSC (2010): Primary 11E45
DOI: https://doi.org/10.1090/spmj/1382
Published electronically: January 29, 2016
MathSciNet review: 3444459
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Abstract: The Epstein zeta function $ \zeta _3$ of the quadratic form $ x^2+y^2+z^2$ is considered. Information is presented about the results of calculating the zeros of $ \zeta _3$ and of its derivative $ \zeta '_3$. A general setting is suggested for the problem about the distribution of the real parts of the zeros for $ L$-functions on the real line.


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Additional Information

N. V. Proskurin
Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: np@pdmi.ras.ru

DOI: https://doi.org/10.1090/spmj/1382
Keywords: Zeta functions of quadratic forms, distribution of zeros
Received by editor(s): April 16, 2014
Published electronically: January 29, 2016
Article copyright: © Copyright 2016 American Mathematical Society