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    Rights statement: The final publication is available at Springer via https://doi.org/10.1007/s00209-018-2099-9

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On mean values of mollifiers and L-functions associated to primitive cusp forms

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On mean values of mollifiers and L-functions associated to primitive cusp forms. / Kühn, Patrick; Robles, Nicolas; Zeindler, Dirk.

In: Mathematische Zeitschrift, Vol. 291, No. 1-2, 01.02.2019, p. 661-709.

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Kühn, Patrick ; Robles, Nicolas ; Zeindler, Dirk. / On mean values of mollifiers and L-functions associated to primitive cusp forms. In: Mathematische Zeitschrift. 2019 ; Vol. 291, No. 1-2. pp. 661-709.

Bibtex

@article{46d0873a7436482cb36dfd9af8ac2075,
title = "On mean values of mollifiers and L-functions associated to primitive cusp forms",
abstract = "We study the second moment of the L-function associated to a holomorphic primitive cusp form of even weight perturbed by a new family of mollifiers. This family is a natural extension of the mollifers considered by Conrey and by Bui, Conrey and Young. As an application, we improve the current lower bound on critical zeros of holomorphic primitive cusp forms.",
keywords = "Dirichlet polynomial, mollifier, Zeros on the critical line, Ratios conjecture technique, autocorrelation, holomorphic cusp form, modular forms, generalized Mobius functions",
author = "Patrick K{\"u}hn and Nicolas Robles and Dirk Zeindler",
note = "https://doi.org/10.1007/s00209-018-2099-9",
year = "2019",
month = feb,
day = "1",
doi = "10.1007/s00209-018-2099-9",
language = "English",
volume = "291",
pages = "661--709",
journal = "Mathematische Zeitschrift",
issn = "0025-5874",
publisher = "Springer New York",
number = "1-2",

}

RIS

TY - JOUR

T1 - On mean values of mollifiers and L-functions associated to primitive cusp forms

AU - Kühn, Patrick

AU - Robles, Nicolas

AU - Zeindler, Dirk

N1 - https://doi.org/10.1007/s00209-018-2099-9

PY - 2019/2/1

Y1 - 2019/2/1

N2 - We study the second moment of the L-function associated to a holomorphic primitive cusp form of even weight perturbed by a new family of mollifiers. This family is a natural extension of the mollifers considered by Conrey and by Bui, Conrey and Young. As an application, we improve the current lower bound on critical zeros of holomorphic primitive cusp forms.

AB - We study the second moment of the L-function associated to a holomorphic primitive cusp form of even weight perturbed by a new family of mollifiers. This family is a natural extension of the mollifers considered by Conrey and by Bui, Conrey and Young. As an application, we improve the current lower bound on critical zeros of holomorphic primitive cusp forms.

KW - Dirichlet polynomial

KW - mollifier

KW - Zeros on the critical line

KW - Ratios conjecture technique

KW - autocorrelation

KW - holomorphic cusp form

KW - modular forms

KW - generalized Mobius functions

U2 - 10.1007/s00209-018-2099-9

DO - 10.1007/s00209-018-2099-9

M3 - Journal article

VL - 291

SP - 661

EP - 709

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 1-2

ER -