CONVERGENCE OF DIRICHLET SERIES AND EULER PRODUCTS

Autor:	Doug S. Phillips, Peter Zvengrowski
Rok vydání:	2017
Předmět:	symbols.namesake Convergence (routing) symbols Euler's formula Applied mathematics General Medicine Dirichlet series Mathematics
Zdroj:	Contributions, Section of Natural, Mathematical and Biotechnical Sciences. 38:153
ISSN:	1857-9949 1857-9027
DOI:	10.20903/csnmbs.masa.2017.38.2.111
Popis:	The first part of this paper deals with Dirichlet series, and convergence theorems are proved that strengthen the classical convergence theorem as found e.g. in Serre’s “A Course in Arithmetic.” The second part deals with Euler-type products. A convergence theorem is proved giving sufficient conditions for such products to converge in the half-plane having real part greater than 1/2. Numerical evidence is also presented that suggests that the Euler products corresponding to Dirichlet L-functions L(s, χ), where χ is a primitive Dirichlet character, converge in this half-plane.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b90a7120231414b9f7988702427b11db https://doi.org/10.20903/csnmbs.masa.2017.38.2.111 Zobrazit plný text záznamu