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 $F(s)$.
Publié le : 1999-07-04
Classification:
mean-value,
short-intervals,
maximum-modulus principle,
Hadamard three circles theorem,
Ingham lines,
Dirichlet series,
Poles,
[MATH]Mathematics [math]
@article{hal-01109602,
author = {Balasubramanian, R and Ramachandra, K and Sankaranarayanan, A and Srinivas, K},
title = {Notes on the Riemann zeta Function-III},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01109602}
}
Balasubramanian, R; Ramachandra, K; Sankaranarayanan, A; Srinivas, K. Notes on the Riemann zeta Function-III. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-01109602/