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arXiv:1206.1679 [math.NT]AbstractReferencesReviewsResources

Distinct zeros and simple zeros of Dirichlet $L$-functions

Wu Xiaosheng

Published 2012-06-08, updated 2013-11-17Version 4

In this paper, we study the number of additional zeros of Dirichlet $L$-function caused by multiplicity by using Asymptotic Large Sieve. Then in asymptotic terms we prove that there are more than 80.124% of zeros of the family of Dirichlet $L$-functions are distinct and more than 60.248% of zeros of the family of Dirichlet $L$-functions are simple. In addition, assuming the Generalized Riemann Hypothesis, we improve these proportions to 83.216% and 66.433%.

Comments: arXiv admin note: text overlap with arXiv:1206.3737
Categories: math.NT
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