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Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli

Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli

Using the method of multiple Dirichlet series, we develop L-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for quadratic families of Dirichlet and Hecke L-functions of primerelated moduli of imaginary quadratic number fields of class number one under the generalized Riemann hypothesis. As …