Geodesic
On the Error Term in Duke's Estimate for the Average Special Value of L-Functions
Canadian mathematical bulletin, Tome 48 (2005) no. 4, pp. 535-546

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DOI

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 $O\left( {{N}^{-1/2}}\log N \right)$ .
DOI : 10.4153/CMB-2005-049-8
Mots-clés : 11F67, 11F11 
Ellenberg, Jordan S. On the Error Term in Duke's Estimate for the Average Special Value of L-Functions. Canadian mathematical bulletin, Tome 48 (2005) no. 4, pp. 535-546. doi: 10.4153/CMB-2005-049-8
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     title = {On the {Error} {Term} in {Duke's} {Estimate} for the {Average} {Special} {Value} of {L-Functions}},
     journal = {Canadian mathematical bulletin},
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     year = {2005},
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     doi = {10.4153/CMB-2005-049-8},
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