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On the Error Term in Duke's Estimate for the Average Special Value of L-Functions

Published online by Cambridge University Press:  20 November 2018

Jordan S. Ellenberg
Jordan S. Ellenberg*
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08844, U.S.A. e-mail: ellenber@math.princeton.edu
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Abstract

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Let $\mathcal{F}$ be an orthonormal basis for weight 2 cusp forms of level $N$. We show that various weighted averages of special values $L\left( f\otimes \text{ }\!\!\chi\!\!\text{ ,1} \right)$ over $f\in \mathcal{F}$ are equal to $4\text{ }\!\!\pi\!\!\text{ }c+O\left( {{N}^{-1+\in }} \right)$, where $c$ is an explicit nonzero constant. A previous result of Duke gives an error term of $O\left( {{N}^{-1/2}}\log N \right)$.

Keywords

11F6711F11
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 4 , 01 December 2005 , pp. 535 - 546
Copyright
Copyright © Canadian Mathematical Society 2005

References

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