On the value-distribution of Epstein zeta-functions.

Jörn Steuding

Publicacions Matemàtiques (2007)

  • Volume: 51, Issue: Extra, page 221-244
  • ISSN: 0214-1493

Abstract

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We investigate the value-distribution of Epstein zeta-functions ζ(s; Q), where Q is a positive definite quadratic form in n variables. We prove an asymptotic formula for the number of c-values, i.e., the roots of the equation ζ(s; Q) = c, where c is any fixed complex number. Moreover, we show that, in general, these c-values are asymmetrically distributed with respect to the critical line Re s =n/4. This complements previous results on the zero-distribution.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].

How to cite

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Steuding, Jörn. "On the value-distribution of Epstein zeta-functions.." Publicacions Matemàtiques 51.Extra (2007): 221-244. <http://eudml.org/doc/41924>.

@article{Steuding2007,
abstract = {We investigate the value-distribution of Epstein zeta-functions ζ(s; Q), where Q is a positive definite quadratic form in n variables. We prove an asymptotic formula for the number of c-values, i.e., the roots of the equation ζ(s; Q) = c, where c is any fixed complex number. Moreover, we show that, in general, these c-values are asymmetrically distributed with respect to the critical line Re s =n/4. This complements previous results on the zero-distribution.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].},
author = {Steuding, Jörn},
journal = {Publicacions Matemàtiques},
keywords = {Teoría de números; Función zeta; Series de Dirichlet; Formas cuadráticas; Teoría de Nevanlinna; Epstein zeta-functions; quadratic forms; value-distribution; Nevanlinna theory},
language = {eng},
number = {Extra},
pages = {221-244},
title = {On the value-distribution of Epstein zeta-functions.},
url = {http://eudml.org/doc/41924},
volume = {51},
year = {2007},
}

TY - JOUR
AU - Steuding, Jörn
TI - On the value-distribution of Epstein zeta-functions.
JO - Publicacions Matemàtiques
PY - 2007
VL - 51
IS - Extra
SP - 221
EP - 244
AB - We investigate the value-distribution of Epstein zeta-functions ζ(s; Q), where Q is a positive definite quadratic form in n variables. We prove an asymptotic formula for the number of c-values, i.e., the roots of the equation ζ(s; Q) = c, where c is any fixed complex number. Moreover, we show that, in general, these c-values are asymmetrically distributed with respect to the critical line Re s =n/4. This complements previous results on the zero-distribution.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
LA - eng
KW - Teoría de números; Función zeta; Series de Dirichlet; Formas cuadráticas; Teoría de Nevanlinna; Epstein zeta-functions; quadratic forms; value-distribution; Nevanlinna theory
UR - http://eudml.org/doc/41924
ER -

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