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



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Muñoz, Vicente and Marcos Peréz, Ricardo (2015) Unified Treatment of Explicit and Trace Formulas via Poisson-Newton Formula. Communications in Mathematical Physics, 336 (3). pp. 1201-1230. ISSN 0010-3616

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Official URL: http://link.springer.com/article/10.1007%2Fs00220-015-2312-1


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.

Item Type:Article
Uncontrolled Keywords:Dirichlet series; Poisson formula; Explicit formula; Trace Formula
Subjects:Sciences > Mathematics > Number theory
ID Code:30122
Deposited On:18 May 2015 08:12
Last Modified:12 Dec 2018 15:12

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