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Extreme values of symmetric power L-functions at 1

Extreme values of symmetric power L-functions at 1

We obtain an almost all result on the size of the symmetric mth power L-functions (m = 1, 2, 3, 4) for the normalized Hecke eigencuspforms at s = 1, which extends results of Elliott and Montgomery & Vaughan on Dirichlet L-functions to higher degree L-functions.