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arXiv · 1901.10790

Symmetry of zeros of Lerch zeta-function for equal parameters

Ramūnas Garunkštis·Rokas Tamošiūnas
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Abstract

For most values of parameters $λ$ and $α$, the zeros of the Lerch zeta-function $L(λ, α, s)$ are distributed very chaotically. In this paper we consider the special case of equal parameters $L(λ, λ, s)$ and show by calculations that the nontrivial zeros either lie extremely close to the critical line $σ= 1/2$ or are distributed almost symmetrically with respect to the critical line. We also investigate this phenomenon theoretically.

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Ramūnas Garunkštis, Rokas Tamošiūnas. 2019-01-30. Symmetry of zeros of Lerch zeta-function for equal parameters. https://arxiv.org/abs/1901.10790

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