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QUANTITATIVE ESTIMATES FOR SIMPLE ZEROS OF $L$-FUNCTIONS

Part of: Discontinuous groups and automorphic forms Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  07 January 2019

Andrew R. Booker ,
Micah B. Milinovich  and
Nathan Ng
Andrew R. Booker
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, U.K. email andrew.booker@bristol.ac.uk
Micah B. Milinovich
Affiliation:
Department of Mathematics, University of Mississippi, University, MS 38677, U.S.A. email mbmilino@olemiss.edu
Nathan Ng
Affiliation:
Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB T1K 3M4, Canada email nathan.ng@uleth.ca
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Abstract

We generalize a method of Conrey and Ghosh [Simple zeros of the Ramanujan $\unicode[STIX]{x1D70F}$-Dirichlet series. Invent. Math. 94(2) (1988), 403–419] to prove quantitative estimates for simple zeros of modular form $L$-functions of arbitrary conductor.

MSC classification

Primary: 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations 11F11: Holomorphic modular forms of integral weight 11M41: Other Dirichlet series and zeta functions

Information

Type
Research Article
Information
Mathematika , Volume 65 , Issue 2 , 2019 , pp. 375 - 399
Copyright
Copyright © University College London 2019 

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Footnotes

Research of the first author was supported by EPSRC Grant EP/K034383/1. Research of the second author was supported by the NSA Young Investigator Grants H98230-15-1-0231 and H98230-16-1-0311. Research of the third author was supported by NSERC Discovery Grant (RGPIN-2015-05972). No data were created in the course of this study.

References

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