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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Some numerical computations concerning spinor zeta functions in genus $\boldsymbol{2}$ at the central point


Authors: Winfried Kohnen and Michael Kuß
Journal: Math. Comp. 71 (2002), 1597-1607
MSC (2000): Primary 11F46
Published electronically: December 5, 2001
MathSciNet review: 1933046
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Abstract: We numerically compute the central critical values of odd quadratic character twists with respect to some small discriminants $D$ of spinor zeta functions attached to Seigel-Hecke eigenforms $F$ of genus 2 in the first few cases where $F$ does not belong to the Maass space. As a result, in the cases considered we can numerically confirm a conjecture of Böcherer, according to which these central critical values should be proportional to the squares of certain finite sums of Fourier coefficients of $F$.


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Additional Information

Winfried Kohnen
Affiliation: Universität Heidelberg, Mathematisches Institut, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
Email: winfried@mathi.uni-heidelberg.de

Michael Kuß
Affiliation: Universität Heidelberg, Mathematisches Institut, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
Email: michael.kuss@urz.uni-heidelberg.de

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01399-0
PII: S 0025-5718(01)01399-0
Received by editor(s): October 20, 1999
Received by editor(s) in revised form: January 3, 2001
Published electronically: December 5, 2001
Article copyright: © Copyright 2001 American Mathematical Society