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)].
@article{urn:eudml:doc:41924,
title = {On the value-distribution of Epstein zeta-functions.},
journal = {Publicacions Matem\`atiques},
year = {2007},
pages = {221-244},
zbl = {1183.11057},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41924}
}
Steuding, Jörn. On the value-distribution of Epstein zeta-functions.. Publicacions Matemàtiques, (2007), pp. 221-244. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41924/