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On the Error Term in Duke's Estimate for the Average Special Value of $L$-Functions |
Canad. Math. Bull. 48(2005), 535-546
E-Published:
2005-12-01
Printed: Dec 2005
Printed: Dec 2005
- Jordan S. Ellenberg
Abstract
Let cal F be an orthonormal basis for weight 2
cusp forms of level N. We show that various weighted averages of
special values L(f tensor chi, 1) over f \in cal F are equal to 4 π c + O(N-1 + epsilon), where c is an explicit nonzero constant. A previous result of Duke gives an error
term of O(N-1/2log N).
| MSC Classifications: |
11F67 - Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11F11 - Holomorphic modular forms of integral weight |