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Mathematics of Computation

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Values of symmetric cube $ L$-functions and Fourier coefficients of Siegel Eisenstein series of degree-3


Author: Dominic Lanphier
Journal: Math. Comp. 80 (2011), 409-428
MSC (2010): Primary 11F67, 11F46, 11F30
DOI: https://doi.org/10.1090/S0025-5718-10-02350-1
Published electronically: April 15, 2010
MathSciNet review: 2728987
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Abstract: We obtain formulas for certain weighted sums of values of the symmetric square and triple product $ L$-functions. As a consequence, we get exact values at the right critical point for the symmetric square and symmetric cube $ L$-functions attached to certain cuspforms. We also give applications to Fourier coefficients of modular forms.


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Additional Information

Dominic Lanphier
Affiliation: Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101
Email: dominic.lanphier@wku.edu

DOI: https://doi.org/10.1090/S0025-5718-10-02350-1
Received by editor(s): April 20, 2009
Received by editor(s) in revised form: August 27, 2009
Published electronically: April 15, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.