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# Strong Multiplicity One for the Selberg Class

Published:2004-09-01
Printed: Sep 2004
• K. Soundararajan
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## Abstract

We investigate the problem of determining elements in the Selberg class by means of their Dirichlet series coefficients at primes.
 MSC Classifications: 11M41 - Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72} 11M26 - Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses 11M06 - $\zeta (s)$ and $L(s, \chi)$