An explicit formula for the zeros of the Rankin-Selberg L -function via the projection of C ∞ -modular forms

Takumi Noda
2008 Kodai Mathematical Journal  
In this report, we describe one explicit formula for the zeros of the Rankin-Selberg L-function by using the projection of the $c^{\infty}$ -automorphic forms [Noda, (Kodal. Math. J. 2008)]. The projection was introduced by [Sturm (Duke Math. J. 1981)] in the study of the special values of automorphic L-functions. Combining the idea of [Zagier (Springer, 1981, Proposition 3) $]$ and the integral transformation of the confluent hypergeometric function, we derive an explicit fomiula which
more » ... miula which correlates the zeros of the zeta-function and the Hecke eigenvalues. The main theorem contains the case of the symmetric square L-function, that first appeared in author's previous paper [Noda, (Acta. Arith. 1995)].
doi:10.2996/kmj/1206454556 fatcat:3hd767e53zcczpjhc7fofx7blm