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A NOTE ON SIMPLE ZEROS OF PRIMITIVE DIRICHLET $L$-FUNCTIONS
Published online by Cambridge University Press: 08 July 2015
Abstract
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.
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- © 2015 Australian Mathematical Publishing Association Inc.
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