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Inhomogeneous multidimensional Epstein zeta functions

Journal of Mathematical Physics, 1991
The pole structure of the inhomogeneous multidimensional Epstein zeta function, Em2N(s; a1,...,aN)=∑∞n1,...,nN =1 (a1n21+⋅⋅⋅+aNn2N +m2)−s, is determined using heat-kernel techniques. The poles of Em2N(s; a1,...,aN) are found to be s=N/2; (N−1)/2;...; (1)/(2) ; −(2l+1)/2, l∈ 𝒩0.
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Local minima of the Epstein zeta-function

Mathematical Notes of the Academy of Sciences of the USSR, 1989
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Zeros of Epstein's Zeta-Functions

Proceedings of the London Mathematical Society, 1935
Potter, H. S. A., Titchmarsh, E. C.
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On Epstein's Zeta-Function

Proceedings of the London Mathematical Society, 1934
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A Bohr–Jessen Type Theorems for the Epstein Zeta-Function: III

Results in Mathematics, 2021
Antanas Laurincikas, Renata Macaitienė
exaly  

On the mean square of the Epstein zeta-function

2019
We consider the second power moment of the Epstein zeta-function and construct the asymptotic formula in special case, when ?????(u,v) = u?? + Av?? , A > 0, A ??? 1, 2(mod 4) and ??0(u,v) belongs to the one-class kind G??? of the quadratic forms of discriminant ???4A.
Savastru, O.V., Varbanets, P.D.
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Generation of off-critical zeros for hypercubic Epstein zeta functions

Applied Mathematics and Computation, 2022
Ladislav Šamaj
exaly  

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