Some numerical computations concerning spinor zeta functions in genus 2 at the central point

Kohnen, Winfried; Kuß, Michael

doi:10.1090/S0025-5718-01-01399-0

Some numerical computations concerning spinor zeta functions in genus $\boldsymbol {2}$ at the central point
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by Winfried Kohnen and Michael Kuß;

Math. Comp. 71 (2002), 1597-1607

DOI: https://doi.org/10.1090/S0025-5718-01-01399-0

Published electronically: December 5, 2001

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