EuDML | Browse

Let $F$ be a class of entire functions represented by Dirichlet series with complex frequencies $\sum a_{k} e^{〈 λ^{k}, z 〉}$ for which $(| λ^{k} {| / e)}^{| λ^{k} |} k! | a_{k} |$ is bounded. Then $F$ is proved to be a commutative Banach algebra with identity and it fails to become a division algebra. $F$ is also proved to be a total set. Conditions for the existence of inverse, topological zero divisor and continuous linear functional for any element belonging to $F$ have also been established.

Absolutely convergent Dirichlet series and analytic continuation of its sum.

Korobeĭnik, Yu.F. (1998)

Lobachevskii Journal of Mathematics

Addendum to the paper " On the zeros of a class of generalized Dirichlet series".

K. Ramachandra (1975)

Journal für die reine und angewandte Mathematik

An algorithm for nonharmonic signal analysis using Dirichlet series on convex polygons.

Forster, Brigitte (2002)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

An estimate for the Dirichlet series in a half-strip in the case of the irregular distribution of exponents. II.

Gaĭsin, A.M., Sergeeva, D.I. (2008)

Sibirskij Matematicheskij Zhurnal

An estimate for the Dirichlet series with Fejér gaps on the real axis.

Gajsin, A.M., Latypov, I.D. (2004)

Sibirskij Matematicheskij Zhurnal

Analytic continuation of Dirichlet series.

J. Milne Anderson, Dimitry Khavinson, Harold S. Shapiro (1995)

Revista Matemática Iberoamericana

The questions considered in this paper arose from the study [KS] of I. Fredholm's (insufficient) proof that the gap series Σ0∞ an ζn2 (where 0 < |a| < 1) is nowhere continuable across {|ζ| = 1}. The interest of Fredholm's method ([F],[ML]) is not so much its efficacy in proving gap theorems (indeed, much more general results can be got by other means, cf. the Fabry gap theorem in [Di]) as in the connection it made between certain special gap series and partial differential equations...

Applications arithmétiques de l'étude des valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme

Philippe Cassou-Noguès (1981)

Annales de l'institut Fourier

Nous étudions les fonctions $p$ -adiques associées à des séries du type $Z (P, Q, ξ) (s) = \sum_{n \in N^{r}} Q (n) ξ^{n} P (n)^{- s}$ dans certains cas, où elles admettent un prolongement méromorphe à $C$ avec un nombre fini de pôles et des valeurs aux entiers négatifs algébriques. On retrouve comme cas particulier les fonctions $L$ $p$ -adiques des corps totalement réels et les fonctions $Γ$ -multiples $p$ -adiques.

Arithmetic mean function of the real part of entire Dirichlet series I

J. S. Gupta, Shakti Bala (1975)

Annales Polonici Mathematici

Arithmetical properties of finite rings and algebras, and analytical number theory. V. Categories and relative analytic number theory.

John Knopfmacher (1974)

Journal für die reine und angewandte Mathematik

Currently displaying 1 – 14 of 14

Page 1