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Modular-type relations associated to the Rankin-Selberg \(L\)-function. (English) Zbl 1422.11175

Summary: J. L. Hafner and J. Stopple [Ramanujan J. 4, No. 2, 123–128 (2000; Zbl 0987.11055)] proved a conjecture of Zagier relating to the asymptotic behaviour of the inverse Mellin transform of the symmetric square \(L\)-function associated with the Ramanujan tau function. In this paper, we prove a similar result for any cusp form over the full modular group.

MSC:

11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
11N37 Asymptotic results on arithmetic functions

Citations:

Zbl 0987.11055
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References:

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