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- Title
First moment of central values of quadratic Hecke L-functions in the Gaussian field.
- Authors
Gao, Peng; Zhao, Liangyi
- Abstract
We evaluate the smoothed first moment of central values of a family of quadratic Hecke L -functions in the Gaussian field using the method of double Dirichlet series. The asymptotic formula we obtain has an error term of size O (X 1 / 4 + ) under the generalized Riemann hypothesis. The same approach also allows us to obtain asymptotic formulas for all X , Y for a smoothed double character sum involving ∑ N (m) ≤ X , N (n) ≤ Y (m n) , where (⋅ n) denotes the quadratic symbol in the Gaussian field.
- Subjects
L-functions; RIEMANN hypothesis; DIRICHLET series; FAMILY values; QUADRATIC equations
- Publication
International Journal of Number Theory, 2023, Vol 19, Issue 7, p1621
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042123500793