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Dirichlet approximation and universal Dirichlet series
[article]

2016
*
arXiv
*
pre-print

We also strengthen the notion of universal

arXiv:1608.06457v1
fatcat:q3wirkj4wfe3fhgeepq54vhux4
*Dirichlet**series*. ... We characterize the uniform limits of*Dirichlet*polynomials on a right half plane. ... Thus all*Dirichlet**series*of f coincide on C + . ...##
###
Automatic Dirichlet Series

2000
*
Journal of Number Theory
*

*Dirichlet*

*series*whose coefficients are generated by finite automata define meromorphic functions on the whole complex plane. ... For another interesting similar class of

*Dirichlet*

*series*, namely

*Dirichlet*

*series*of (completely) d-multiplicative sequences, see [12] . ...

*DIRICHLET*

*SERIES*OF AUTOMATIC SEQUENCES With a sequence (u n ) n 0 taking its values in C we associate two

*Dirichlet*

*series*given by If the sequence (u n ) n 0 takes only finitely many values (this is ...

##
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Series de Dirichlet

2008
*
Revista de Educación Matemática
*

Las

doaj:2e72a710cd9142abbf05abab6503beda
fatcat:uolh6v7ruzhqhol4kdlwvbjtve
*series*de*Dirichlet*asociadas a caracteres de*Dirichlet*son llamadas L-*series*, y se denotan L(s, χ) donde χ es un caracter de*Dirichlet*. ... Sea F (s) = f (n)n −s una*serie*de*Dirichlet*. ... − L (s, χ) L(s, χ) = − d ds (log L(s, χ)) = d ds Teorema de*Dirichlet*Usaremos la notación de congruencias. Notemos que n es de la forma qN + r si y sólo si n ≡ r (mód N ) . ...##
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Admissible Dirichlet Series
[article]

2005
*
arXiv
*
pre-print

We propose a definition of "Admissible

arXiv:math/0507487v1
fatcat:s6xr4snjgzc53l6sfxs4qfcaze
*Dirichlet**Series*" as the analog of Hayman's 1956 definition of "Admissible Power*Series*". ... In this paper a notion of admissibility for functions that have*Dirichlet**series*expansions is proposed. ... It is clear that each F k (s) satisfies (A1)-(A3), and has a*Dirichlet**series*expansion with abscissa of convergence α = 0. ...##
###
Note on Dirichlet Series. IV. On the Singularities of Dirichlet Series

1953
*
Proceedings of the American Mathematical Society
*

If lim»^« log n/X" = 0, then there exists a

doi:10.2307/2031809
fatcat:ujyrnn7h4zdtdhki25f4mhv53q
*Dirichlet**series*X/"-i &» exp (-Xns) having o-= o-, as the natural boundary such that arg (6")=arg (a") (» = 1, 2, ■ ■ ■), and lim«..«, \bn/a"\ =1.Proof. ...##
###
Note on Dirichlet series. IV. On the singularities of Dirichlet series

1953
*
Proceedings of the American Mathematical Society
*

If lim»^« log n/X" = 0, then there exists a

doi:10.1090/s0002-9939-1953-0053263-x
fatcat:yhcehvo6ajbsjb5u6kxdw537ai
*Dirichlet**series*X/"-i &» exp (-Xns) having o-= o-, as the natural boundary such that arg (6")=arg (a") (» = 1, 2, ■ ■ ■), and lim«..«, \bn/a"\ =1.Proof. ...##
###
On lacunary Dirichlet series

1950
*
Proceedings of the American Mathematical Society
*

Let us take for the constants X*, 0<o<o<l <4<9< from a well known theorem concerning restricted overconvergence of

doi:10.1090/s0002-9939-1950-0036836-7
fatcat:d3oc6fystrhy7dmne7s2qn4exi
*Dirichlet**series*, see [l, p. 141], that there exists an increasing sequence of integers ... License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use on lacunary*dirichlet**series*License or copyright restrictions may apply to redistribution ...##
###
Shifted Multiple Dirichlet Series
[article]

2014
*
arXiv
*
pre-print

We develop certain aspects of the theory of shifted multiple

arXiv:1412.5917v1
fatcat:c3q3yasuufewdajfgvtboccjsa
*Dirichlet**series*and study their meromorphic continuations. ... This*series*can be transformed as a*Dirichlet**series*given in (4.10). ...*Dirichlet**series*are dealt with as complete objects, and are used to build shifted multiple*Dirichlet**series*in several variables. ...##
###
Sulle serie di dirichlet

1915
*
Rendiconti del circolo matematico di Palermo
*

di

doi:10.1007/bf03014842
fatcat:hufezkacnrectkavicanhtfwdq
*DIRICHLET*cir. ... In particolare, il prodotto di n*serie*di*DIRICHLET*convergenti in tutto il piano, n-I delle quali hanno un semipiano di convergenza assoluta, ~ in tutto il piano sommabile del prim'ordine. ...##
###
Dirichlet and Poincaré series

1985
*
Glasgow Mathematical Journal
*

Let L je (s) denote the

doi:10.1017/s0017089500006066
fatcat:rdek6yseofaw5bcgvtfsqxxrtu
*Dirichlet**series*attached to F= F} and £ as in (6) and (7) . ... The associated*Dirichlet**series*oo L £ (s) = £ a«(n)n" s , s = a + if, ffl S (^) k S k -s ) , (9) where F(s) denotes the gamma function. ... In Theorem 2 certain combinations of the*Dirichlet**series*attached to cusp forms are expressed by*series*which, in contrast to the*Dirichlet**series*, converge absolutely inside the critical strip. ...##
###
On Lacunary Dirichlet Series

1950
*
Proceedings of the American Mathematical Society
*

Let us take for the constants X*, 0<o<o<l <4<9< from a well known theorem concerning restricted overconvergence of

doi:10.2307/2032321
fatcat:pzkmfxjhfzhdvfwsoytj2aia2i
*Dirichlet**series*, see [l, p. 141], that there exists an increasing sequence of integers ... License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use on lacunary*dirichlet**series*License or copyright restrictions may apply to redistribution ...##
###
Introduction: Multiple Dirichlet Series
[chapter]

2012
*
Multiple Dirichlet Series, L-functions and Automorphic Forms
*

In the theory of multiple

doi:10.1007/978-0-8176-8334-4_1
fatcat:tkgfrjuvejbbradofp3l6chqbe
*Dirichlet**series*it might be useful to substituteW w for the p-part at a finite number of places. ... Despite the similarity of this multiple*Dirichlet**series*to that of [36] , this*series*does not fit the same way in the theory of Weyl group multiple*Dirichlet**series*. ... If the a n are themselves L-functions or other*Dirichlet**series*, this is then a multiple*Dirichlet**series*. One may try to study moments of L-functions this way. ...##
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On Kubota's Dirichlet series

2006
*
Journal für die Reine und Angewandte Mathematik
*

The basic building blocks in the Weyl group multiple

doi:10.1515/crelle.2006.073
fatcat:x7uamuykorgjbpdbtmeu4efxua
*Dirichlet**series*are the Kubota*Dirichlet**series*. ... The Kubota*Dirichlet**series*are the entry point to a fascinating universe. ... • We exhibit concrete finite-dimensional families of*Dirichlet**series*that are closed under the functional equations. The description of these*Dirichlet**series*is as simple as we can imagine. ...##
###
Dirichlet series and series with Stirling numbers
[article]

2021
*
arXiv
*
pre-print

This paper presents a number of identities for

arXiv:2109.09167v2
fatcat:flu2xxtdl5gmhe3vmyoctmqyia
*Dirichlet**series*and*series*with Stirling numbers of the first kind. ... As coefficients for the*Dirichlet**series*we use Cauchy numbers of the first and second kinds, hyperharmonic numbers, derangement numbers, binomial coefficients, central binomial coefficients, and Catalan ... They are defined by the Example 5 . 5*Dirichlet**series*with derangement numbers. ...##
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The multiple Dirichlet product and the multiple Dirichlet series

2017
*
International Journal of Number Theory
*

u^{*}(1)=1\neq 0$ $u^{*}\in$ $U$ $u^{*}$ 2.2 $u_{EZ}$ $u_{EZ}(1)=0$ $u_{EZ}\not\in U$ 2.2

doi:10.1142/s1793042117501184
fatcat:2alb6fulvnbkbc7y5p6tmkhspq
*Dirichlet*$F(s_{1}, \ldots, s_{k};f)$ $f\in U$ Euler-Zagier 3*Dirichlet*2*Dirichlet**Dirichlet*1*Dirichlet*Theorem3.1 ... .$*Dirichlet*$*$ $(f*g)(n)= \sum_{a\cdot b--n,a_{)}b\in \mathbb{N}^{k}}f(a)g(b)$ . $k=1$*Dirichlet**Dirichlet*$k$ $I$ $I(n):=\{\begin{array}{ll}1 (n=1) ,0 (otherwise).\end{array}$ Theorem 2.2. ...
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