Results 1 to 10 of about 101,614 (60)

Subconvexity for a double Dirichlet series [PDF]

Compositio Mathematica, 2009
For Dirichlet series roughly of the type $Z(s, w) = sum_d L(s, chi_d) d^{-w}$ the subconvexity bound $Z(s, w) \ll (sw(s+w))^{1/6+\varepsilon}$ is proved on the critical lines $\Re s = \Re w = 1/2$. The convexity bound would replace 1/6 with 1/4.
Heath-Brown, Valentin Blomer
core   +5 more sources

On Random Multiple Dirichlet Series [PDF]

, 2011
We study the natural boundary of a random Dirichlet series associated with Goldbach numbers.Comment: soumis (2011) 1-
Bhowmik, Gautami, Matsumoto, Kohji
core   +4 more sources

On Dirichlet series and functional equations

Journal of Number Theory, 2017
There exist many explicit evaluations of Dirichlet series. Most of them are constructed via the same approach: by taking products or powers of Dirichlet series with a known Euler product representation.
Kuznetsov, Alexey
core   +3 more sources

A note on abscissas of Dirichlet series [PDF]

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019
Minor revision.
Defant, Andreas, Pérez, Antonio, Sevilla Peris, Pablo   +2 more
openaire   +6 more sources

Series de Dirichlet

Revista de Educación Matemática, 2021
En este artículo estamos interesados en la Teoría Analítica de Números. Ésta tiene diversas maneras tanto de encarar como de resolver problemas. Por ejemplo, a la teoría de números le interesa conocer el comportamiento de ciertas funciones aritméticas (funciones f: N → C), tales como: rk(n) el número de formas de escribir n como suma de k cuadrados; la
openaire   +3 more sources

Double Dirichlet series and quantum unique ergodicity of weight 1/2 Eisenstein series [PDF]

, 2014
The problem of quantum unique ergodicity (QUE) of weight 1/2 Eisenstein series for {\Gamma}_0(4) leads to the study of certain double Dirichlet series involving GL2 automorphic forms and Dirichlet characters.
Bailey, Heath-Brown, Iwaniec, Iwaniec, Luo, Morten Risager, Nicole Raulf, Shnirelman, Yiannis Petridis, Zagier   +9 more
core   +2 more sources

A connection between power series and Dirichlet series

Journal of Mathematical Analysis and Applications, 2021
[EN] We prove that for any convergent Laurent series f(z) = ∞n=−k anzn with k ≥ 0, there is a meromorphic function F(s) on C whose only possible poles are among the integers n = 1, 2, ..., k, having residues Res(F; n) = a−n/(n − 1)!, and satisfying F(−n) = (−1)nn! an for n = 0, 1, 2, ....
Navas, Luis M., Ruiz, Francisco J., Varona, Juan L., 0000-0002-2023-9946   +3 more
openaire   +4 more sources

Weyl group multiple Dirichlet series constructed from quadratic characters [PDF]

, 2006
We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations.
A. Diaconu, B. Brubaker, B. Fisher, B. Fisher, C.L. Siegel, D. Bump, D. Bump, D. Bump, D. Bump, D. Goldfeld, G. Chinta, G. Chinta, Gautam Chinta, K. Soundararajan, Paul E. Gunnells, S. Bochner, S. Friedberg   +16 more
core   +3 more sources

Natural boundaries of Dirichlet series [PDF]

, 2007
We prove some conditions on the existence of natural boundaries of Dirichlet series. We show that generically the presumed boundary is the natural one.
Bhowmik, Gautami, Schlage-Puchta, Jan-Christoph   +1 more
core   +1 more source

Automatic Dirichlet Series

Journal of Number Theory, 2000
AbstractDirichlet series whose coefficients are generated by finite automata define meromorphic functions on the whole complex plane. As consequences, a new proof of Cobham's theorem on the existence of logarithmic frequencies of symbols in automatic sequences is given, and certain infinite products are explicitly computed.
Allouche, J.-P, Mendès France, M, Peyrière, J   +2 more
openaire   +2 more sources