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oai:docta.ucm.es:20.500.14352/346302023-08-11T09:45:59Zcom_20.500.14352_14col_20.500.14352_15

00925njm 22002777a 4500 dc Muñoz, Vicente author Marcos Peréz, Ricardo author 2015 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. 0010-3616 10.1007/s00220-015-2312-1 https://hdl.handle.net/20.500.14352/34630 http://link.springer.com/article/10.1007%2Fs00220-015-2312-1 http://link.springer.com Unified Treatment of Explicit and Trace Formulas via Poisson-Newton Formula