Glasnik Matematicki, Vol. 60, No. 2 (2025), 207-227. \( \)

PAIR CORRELATION OF ZEROS OF DIRICHLET \(L\)-FUNCTIONS AND PROPORTION OF SIMPLE ZEROS

Ramu̅nas Garunkštis and Julija Paliulionytė

Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania
e-mail:ramunas.garunkstis@mif.vu.lt

Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania
e-mail:julija.paliulionyte@mif.stud.vu.lt

Abstract.   Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh obtained an unconditional form of Montgomery's theorem concerning pair correlation of zeros of the Riemann zeta function. They used it to prove that under certain assumptions at least 61.7 percent of the zeros are simple. In this paper, we obtain an analogous theorem for Dirichlet \(L\)-functions and apply it to prove a similar result regarding simple zeros of Dirichlet \(L\)-functions.

2020 Mathematics Subject Classification.   11M06

Key words and phrases.   Dirichlet \(L\)-functions, simple zeros, pair correlation

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https://doi.org/10.3336/gm.60.2.03

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