Ratios conjecture of quartic L-functions of prime moduli
arxiv(2024)
摘要
We apply the method of multiple Dirichlet series to develop L-functions
ratios conjecture with one shift in both the numerator and denominator in
certain ranges for the family of quartic Hecke L-functions of prime moduli
over the Gaussian field under the generalized Riemann hypothesis. As
consequences, we evaluate asymptotically the first moment of central values as
well as the one-level density of the same family of L-functions.
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