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Communications in Mathematical Physics

, Volume 336, Issue 3, pp 1201–1230 | Cite as

Unified Treatment of Explicit and Trace Formulas via Poisson–Newton Formula

  • Vicente MuñozEmail author
  • Ricardo Pérez Marco
Article
  • 132 Downloads

Abstract

We prove that a Poisson–Newton formula, in a broad sense, is associated to each Dirichlet series with a meromorphic extension to the whole complex plane of finite order. These formulas simultaneously generalize the classical Poisson formula and Newton formulas for Newton sums. Classical Poisson formulas in Fourier analysis, explicit formulas in number theory and Selberg trace formulas in Riemannian geometry appear as special cases of our general Poisson–Newton formula.

Keywords

Functional Equation Meromorphic Function Zeta Function Dirichlet Series Trace Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Facultad de MatemáticasUniversidad Complutense de MadridMadridSpain
  2. 2.CNRS, LAGA UMR 7539Université Paris XIIIClémentFrance

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