1. Moments of the Dedekind zeta function and other non-primitiveL-functions
- Author
-
Winston Heap
- Subjects
Pure mathematics ,Conjecture ,Mathematics::Number Theory ,General Mathematics ,010102 general mathematics ,01 natural sciences ,Quadratic equation ,Product (mathematics) ,Order (group theory) ,Asymptotic formula ,Galois extension ,0101 mathematics ,Random matrix ,Dedekind zeta function ,Mathematics - Abstract
We give a conjecture for the moments of the Dedekind zeta function of a Galois extension. This is achieved through the hybrid product method of Gonek, Hughes and Keating. The moments of the product over primes are evaluated using a theorem of Montgomery and Vaughan, whilst the moments of the product over zeros are conjectured using a heuristic method involving random matrix theory. The asymptotic formula of the latter is then proved for quadratic extensions in the lowest order case. We are also able to reproduce our moments conjecture in the case of quadratic extensions by using a modified version of the moments recipe of Conrey et al. Generalising our methods, we then provide a conjecture for moments of non-primitiveL-functions, which is supported by some calculations based on Selberg’s conjectures.
- Published
- 2019