Notes on the Riemann zeta Function-III

R Balasubramanian (1) , K Ramachandra (2) , A Sankaranarayanan (3) , K Srinivas (1)

1 IMSc - Institute of Mathematical Sciences [Chennai]
2 National Institute of advanced studies
3 TIFR - 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 $F(s)$.

Mots clés: Poles; Ingham lines; Dirichlet series; Hadamard three circles theorem; maximum-modulus principle; short-intervals; mean-value

Domaines: Mathématiques [math]

R Balasubramanian, K Ramachandra, A Sankaranarayanan, K Srinivas. Notes on the Riemann zeta Function-III. Hardy-Ramanujan Journal, 1999, Volume 22 - 1999 (3), pp.23-33. ⟨10.46298/hrj.1999.139⟩. ⟨hal-01109602⟩