Publication Date:
2014-02-21
Description:
Assuming the generalized Riemann hypothesis, we show using the asymptotic large sieve that 91% of the zeros of primitive Dirichlet L -functions are simple. This improves on earlier work of Özlük which gives a proportion of at most 86%. We further compute the q -analogue of the Pair Correlation Function F ( α ) averaged over all primitive Dirichlet L -functions in the range | α | 〈 2. Previously such a result was available only when the average included all the characters . As a corollary of our results, we obtain an asymptotic formula for a sum over characters similar to the one encountered in the Barban–Davenport–Halberstam Theorem.
Print ISSN:
0033-5606
Electronic ISSN:
1464-3847
Topics:
Mathematics
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