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

Lanphier, Dominic

doi:10.1090/S0025-5718-10-02350-1

Values of symmetric cube $L$-functions and Fourier coefficients of Siegel Eisenstein series of degree-3
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Math. Comp. 80 (2011), 409-428 Request permission

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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