The twisted mean square and critical zeros of Dirichlet L-functions
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In this work, we obtain an asymptotic formula for the twisted mean square of a Dirichlet L-function with a longer mollifier, whose coefficients are also more general than before. As an application we obtain that, for every Dirichlet L-function, more than 41.72% of zeros are on the critical line and more than 40.74% of zeros are simple and on the critical line. These proportions also improve previous results which were proved only for the Riemann zeta-function.
KeywordsTwisted second moment Kloosterman sum Simple zeros Riemann zeta-function Dirichlet L-function
Mathematics Subject Classification11M26 11M06
We would like to express our heartfelt thanks to the anonymous referee for his careful reading and helpful suggestion.
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