On the ramification set of a positive quadratic form over an algebraic number field
Martin Epkenhans (1994)
Acta Arithmetica
J. Hsia (1973)
Acta Arithmetica
J.-H. Evertse (1983)
Inventiones mathematicae
J.H. Evertse (1984)
Inventiones mathematicae
D. Lewis, Kurt Mahler (1961)
Acta Arithmetica
W. Ljunggren (1971)
Acta Arithmetica
Г.А. Ломадзе (1965)
Matematiceskij sbornik
Khosroshvili, D. (1998)
Georgian Mathematical Journal
Kachakhidze, N. (1998)
Georgian Mathematical Journal
Kachakhidze, N. (2001)
Georgian Mathematical Journal
J. Cassels (1964)
Acta Arithmetica
E. Podsypanin (1975)
Acta Arithmetica
Ludwig Bröcker (1988)
Manuscripta mathematica
Akihiko Yukie (1992)
Mathematische Annalen
Alexander Prestel (1987)
Journal für die reine und angewandte Mathematik
Dasheng Wei (2011)
Acta Arithmetica
Zhi-Hong Sun (1998)
Acta Arithmetica
Ayşe Alaca, Şaban Alaca, Kenneth S. Williams (2006)
Acta Arithmetica
Jörn Steuding (2007)
Publicacions Matemàtiques
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...
G. Myerson (1985)
Mathematische Zeitschrift