Mollification of the fourth moment of Dirichlet \(L\)-functions. (English) Zbl 1454.11159
Summary: We evaluate some twisted fourth moment of Dirichlet \(L\)-functions at the central point \(s={1/2}\) and for prime moduli \(q\). The principal tool is a careful analysis of a shifted convolution problem involving the divisor function using the spectral theory of automorphic forms. Having in mind simultaneous non-vanishing results, we apply our result to establish an asymptotic formula for a mollified fourth moment for this family of \(L\)-functions.
MSC:
| 11M06 | \(\zeta (s)\) and \(L(s, \chi)\) |
| 11M26 | Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses |
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