Signs of high order derivatives for the theta and Epstein zeta functions and application
Abstract
In the 1950s, 1960s and 1988, number theorists Rankin Ran1953, Cassels Cas1959, Ennola Enn1964a, Diananda Dia1964, and Montgomery 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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