On the zeros of the zeta function of the quadratic form 𝑥²+𝑦²+𝑧²

Proskurin, N.

doi:10.1090/spmj/1382

On the zeros of the zeta function of the quadratic form $x^2+y^2+z^2$
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by N. V. Proskurin
Translated by: A. Plotkin

St. Petersburg Math. J. 27 (2016), 177-189

DOI: https://doi.org/10.1090/spmj/1382

Published electronically: January 29, 2016

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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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