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arXiv · 2501.01265

Signs of high order derivatives for the theta and Epstein zeta functions and application

Deng Kaixin·Luo Senping
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Abstract

In the 1950s, 1960s and 1988, number theorists Rankin \cite{Ran1953}, Cassels \cite{Cas1959}, Ennola \cite{Enn1964a}, Diananda \cite{Dia1964}, and Montgomery \cite{Mon1988} derived the signs of first order derivatives of Epstein zeta and theta functions, respectively. In this note, we shall derive the signs of higher order derivatives of such functions. Application to lattice minimization problems will be given.

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Deng Kaixin, Luo Senping. 2025-01-02. Signs of high order derivatives for the theta and Epstein zeta functions and application. https://arxiv.org/abs/2501.01265

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