NOTE ON SIMPLE ZEROS OF PRIMITIVE DIRICHLET L-FUNCTIONS

作者：Sono Keiju^*

来源：Bulletin of the Australian Mathematical Society, 2016, 93(1): 19-30.

DOI：10.1017/S0004972715000623

• primitive Dirichlet L-functions
• simple zeros
• pair correlation formula
• reproducing kernel

In this paper, by using the theory of reproducing kernel Hilbert spaces and the pair correlation formula constructed by Chandee et al. ['Simple zeros of primitive Dirichlet L-functions and the asymptotic large sieve', Q. J. Math. 65(1) (2014), 63-87], we prove that at least 93.22% of low-lying zeros of primitive Dirichlet L-functions are simple in a proper sense, under the assumption of the generalised Riemann hypothesis.

• 出版日期2016-2