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Critical zeros of lacunary $L$-functions

Volume 195 / 2020

J. B. Conrey, H. Iwaniec Acta Arithmetica 195 (2020), 217-268 MSC: Primary 11M20. DOI: 10.4064/aa180813-11-11 Published online: 18 May 2020

Abstract

Assuming the existence of infinitely many exceptional discriminants of quadratic fields, it is shown that the Riemann zeta-function has asymptotically 100% of its zeros on selected segments of the critical line.

Authors

  • J. B. ConreyAmerican Institute of Mathematics
    600 East Brokaw Road
    San Jose, CA 95112, U.S.A.
    and
    School of Mathematics
    University of Bristol
    Bristol BS8 1TW, UK
    e-mail
  • H. IwaniecThe ETH Institute for Theoretical Studies
    Clausiusstrasse 47
    8092 Zürich, Switzerland
    and
    Department of Mathematics
    Rutgers University
    New Brunswick, NJ 08903, U.S.A.
    e-mail

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