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A NOTE ON SIMPLE ZEROS OF PRIMITIVE DIRICHLET
$L$-FUNCTIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 93 / Issue 1 / February 2016
- Published online by Cambridge University Press:
- 08 July 2015, pp. 19-30
- Print publication:
- February 2016
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- Article
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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.
