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Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -