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