In the present work, properties of the Epstein zeta function ζ3(s) associated with the sum of three squares are studied. These properties are the following: the behavior in the critical strip, mean value theorems, the distribution of zeros, and the functional equation of a special type. Some conjectures are advanced. Bibliography: 20 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 371, 2009, pp. 157–170.
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Fomenko, O.M. On Epstein’s zeta function. II. J Math Sci 166, 214–221 (2010). https://doi.org/10.1007/s10958-010-9862-8
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DOI: https://doi.org/10.1007/s10958-010-9862-8