## R Balasubramanian ; K Ramachandra ; A Sankaranarayanan ; K Srinivas - Notes on the Riemann zeta Function-III

hrj:139 - Hardy-Ramanujan Journal, January 1, 1999, Volume 22 - 1999 - https://doi.org/10.46298/hrj.1999.139
Notes on the Riemann zeta Function-III

Authors: R Balasubramanian ; K Ramachandra ; A Sankaranarayanan ; K Srinivas

For a good Dirichlet series $F(s)$ (see Definition in \S1) which is a quotient of some products of the translates of the Riemann zeta-function, we prove that there are infinitely many poles $p_1+ip_2$ in $\Im (s)>C$ for every fixed $C>0$. Also, we study the gaps between the ordinates of the consecutive poles of $F(s)$.

Volume: Volume 22 - 1999
Published on: January 1, 1999
Imported on: March 3, 2015
Keywords: mean-value, short-intervals, maximum-modulus principle, Hadamard three circles theorem, Ingham lines, Dirichlet series,Poles,[MATH] Mathematics [math]