Independence of Hecke zeta functions of finite order over normal fields

Autor:	Maciej Radziejewski
Rok vydání:	2006
Předmět:	Discrete mathematics Pure mathematics Arithmetic zeta function Quadratic integer Applied Mathematics General Mathematics Ideal class group Quadratic field Field (mathematics) Algebraic number field Algebraic number Dedekind zeta function Mathematics
Zdroj:	Transactions of the American Mathematical Society. 359:2383-2394
ISSN:	1088-6850 0002-9947
DOI:	10.1090/s0002-9947-06-04078-5
Popis:	We study oscillations of the remainder term corresponding to the counting functions of the sets of elements with unique factorization length in semigroups of algebraic numbers such as the semigroup of algebraic integers or totally positive algebraic integers in a given normal field K. The results imply existence of oscillations when the exponent of the class group of the semigroup in question is sufficiently large depending on the field's degree. In particular, when K is a quadratic field or a normal cubic field oscillations exist whenever the class group is not isomorphic to C 2 a ⊕ C 3 b ⊕ C 4 c for nonnegative integers a,b,c. The main part of this study is concerned with the problem of multiplicative independence of Hecke zeta functions. We also show that there are infinitely many fields whose Dedekind zeta function has infinitely many nontrivial multiple zeros.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::386ebda3101f2bd3e80ac730ef5e3901 https://doi.org/10.1090/s0002-9947-06-04078-5 Zobrazit plný text záznamu