Convolution formula for the sums of generalized Dirichlet L-functions

• Using the Kuznetsov trace formula, we prove a spectral decomposition for the sums of generalized Dirichlet L-functions. Among applications are an explicit formula relating norms of prime geodesics to moments of symmetric square L-functions and an asymptotic expansion for the average of central values of generalized Dirichlet L-functions.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Generalized Dirichlet L-functions

prime geodesic theorem

Kuznetsov

trace formula

generalized Kloosterman sums

symmetric square

L-functions

mean-value

series

weight

values

Mathematics

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