Notes on the Riemann zeta Function-III

R Balasubramanian; K Ramachandra; A Sankaranarayanan; K Srinivas

doi:10.46298/hrj.1999.139

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-IIIArticle

Authors: R Balasubramanian ¹; K Ramachandra ²; A Sankaranarayanan ³; K Srinivas ¹

1 Institute of Mathematical Sciences [Chennai]
2 National Institute of advanced studies
3 Tata Institute for Fundamental Research

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 $F(s)$.

https://doi.org/10.46298/hrj.1999.139

Source: HAL:hal-01109602v1

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]

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

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