Ratios conjecture for quadratic twist of modular $L$-functions

Abstract

We develop the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular $L$-functions using multiple Dirichlet series under the generalized Riemann hypothesis.

13 pages

References in corpus (1)

• Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field

Cited by in corpus (1)

• Ratios conjecture of cubic $L$-functions of prime moduli