Twisted first moment of central values of primitive quadratic Dirichlet $L$-functions
Volume 219 / 2025
Acta Arithmetica 219 (2025), 101-122
MSC: Primary 11M06; Secondary 11M32
DOI: 10.4064/aa240617-6-11
Published online: 28 February 2025
Abstract
We evaluate the twisted first moment of central values of the family of primitive quadratic Dirichlet $L$-functions using the method of double Dirichlet series together with a recursive argument. Our main result is an asymptotic formula with an error term of size that is the square root of that of the main term.
