Other dirichlet series and zeta functions

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ON THE APPROXIMATE FUNCTIONAL EQUATION FOR ζ²(s) AND OTHER DIRICHLET SERIES

The Quarterly Journal of Mathematics, 1986
Writing the approximate functional equation for $\zeta(s)^2$ as \[ \zeta(s)^2=S(s,x)+\chi(s)^2 S(1-s,y)+R(s,x), \] where $S(s,x)=\sum_{n\leq x}d(n)n^{-\sigma}$, $xy=\tau^2$, $\tau =t/2\pi$ and $\chi(s)=2^s \pi^{s-1} \sin(\pi s/2) \Gamma(1-s),$ the author proves that, if $0\leq \sigma \leq 1$, $t\geq 10$ and $1\leq x,y\leq \tau^2$, then \
openaire +2 more sources

Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values

Ramanujan Journal, 2022
Sarth Chavan, christophe Vignat
exaly

Discrete Approximation by a Dirichlet Series Connected to the Riemann Zeta-Function

Mathematics, 2021
Antanas Laurincikas, Darius Šiaučiūnas +1 more
exaly

Fixed points of the riemann zeta function and dirichlet series

Monatshefte Fur Mathematik, 2022
exaly

Infinite Series Concerning Tails of Riemann Zeta Values

Axioms, 2023
Chunli, Wenchang Chu
exaly

Crandall’s computation of the incomplete Gamma function and the Hurwitz zeta function, with applications to Dirichlet L-series

Applied Mathematics and Computation, 2015
David H Bailey
exaly

Recent progress in Lynch syndrome and other familial colorectal cancer syndromes

Ca-A Cancer Journal for Clinicians, 2018
Patrick M Boland +2 more
exaly