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Tauberian theorems for sum sets

P. Erdös, B. Gordon, L. Rubel, E. Straus (1964)

Acta Arithmetica

Tetra and Didi, the cosmic spectral twins.

Doyle, Peter G., Rossetti, Juan Pablo (2004)

Geometry & Topology

The Adelic Zeta Function Associated to the Space of Binary Cubis Forms. Part I: Global Theory.

David J. Wright (1985)

Mathematische Annalen

The analytic continuation and the order estimate of multiple Dirichlet series

Kohji Matsumoto, Yoshio Tanigawa (2003)

Journal de théorie des nombres de Bordeaux

Multiple Dirichlet series of several complex variables are considered. Using the Mellin-Barnes integral formula, we prove the analytic continuation and an upper bound estimate.

The average order of a class of arithmetic functions over arithmetic progressions with applications to quadratic forms.

Robert A. Smith (1980)

Journal für die reine und angewandte Mathematik

The Beurling-Nyman criterion for the Riemann hypothesis: numerical aspects. (Le critère de Beurling et Nyman pour l'hypothèse de Riemann: aspects numérique.)

Landreau, Bernard, Richard, Florent (2002)

Experimental Mathematics

The Bohr inequality for ordinary Dirichlet series

R. Balasubramanian, B. Calado, H. Queffélec (2006)

Studia Mathematica

We extend to the setting of Dirichlet series previous results of H. Bohr for Taylor series in one variable, themselves generalized by V. I. Paulsen, G. Popescu and D. Singh or extended to several variables by L. Aizenberg, R. P. Boas and D. Khavinson. We show in particular that, if $f (s) = \sum_{n = 1}^{\infty} a ₙ n^{- s}$ with ${| | f | |}_{\infty} : = s u p_{ℜ s > 0} | f (s) | < \infty$ , then $\sum_{n = 1}^{\infty} | a ₙ | n^{- 2} {\leq | | f | |}_{\infty}$ and even slightly better, and $\sum_{n = 1}^{\infty} | a ₙ | n^{- 1 / 2} {\leq C | | f | |}_{\infty}$ , C being an absolute constant.