Subconvexity for modular form L-functions in the t aspect

Andrew R. Booker; Micah B. Milinovich; Nathan Ng

doi:10.1016/j.aim.2018.10.037

Subconvexity for modular form L-functions in the t aspect

Andrew R. Booker^*, Micah B. Milinovich, Nathan Ng

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

14 Citations (Scopus)

181 Downloads (Pure)

Abstract

Modifying a method of Jutila, we prove a t-aspect subconvexity estimate for L-functions associated to primitive holomorphic cusp forms of arbitrary level that is of comparable strength to Good's bound for the full modular group, thus improving on a 36-year-old result. A key innovation in our proof is a general form of Voronoi summation that applies to all fractions, even when the level is not squarefree.

Original language	English
Pages (from-to)	299-335
Number of pages	37
Journal	Advances in Mathematics
Volume	341
Early online date	1 Nov 2018
DOIs	https://doi.org/10.1016/j.aim.2018.10.037
Publication status	Published - 7 Jan 2019

Keywords

Subconvexity
Modular forms
L-functions

Access to Document

10.1016/j.aim.2018.10.037

Full-text PDF (accepted author manuscript)
This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at https://www.sciencedirect.com/science/article/pii/S0001870818304316 . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 428 KBLicence: CC BY-NC-ND

Handle.net

Persistent link

Cite this

@article{f38dd5bc3637421bacecfe3957e7636c,

title = "Subconvexity for modular form L-functions in the t aspect",

abstract = "Modifying a method of Jutila, we prove a t-aspect subconvexity estimate for L-functions associated to primitive holomorphic cusp forms of arbitrary level that is of comparable strength to Good's bound for the full modular group, thus improving on a 36-year-old result. A key innovation in our proof is a general form of Voronoi summation that applies to all fractions, even when the level is not squarefree.",

keywords = "Subconvexity, Modular forms, L-functions",

author = "Booker, \{Andrew R.\} and Milinovich, \{Micah B.\} and Nathan Ng",

year = "2019",

month = jan,

day = "7",

doi = "10.1016/j.aim.2018.10.037",

language = "English",

volume = "341",

pages = "299--335",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Subconvexity for modular form L-functions in the t aspect

AU - Booker, Andrew R.

AU - Milinovich, Micah B.

AU - Ng, Nathan

PY - 2019/1/7

Y1 - 2019/1/7

N2 - Modifying a method of Jutila, we prove a t-aspect subconvexity estimate for L-functions associated to primitive holomorphic cusp forms of arbitrary level that is of comparable strength to Good's bound for the full modular group, thus improving on a 36-year-old result. A key innovation in our proof is a general form of Voronoi summation that applies to all fractions, even when the level is not squarefree.

AB - Modifying a method of Jutila, we prove a t-aspect subconvexity estimate for L-functions associated to primitive holomorphic cusp forms of arbitrary level that is of comparable strength to Good's bound for the full modular group, thus improving on a 36-year-old result. A key innovation in our proof is a general form of Voronoi summation that applies to all fractions, even when the level is not squarefree.

KW - Subconvexity

KW - Modular forms

KW - L-functions

UR - http://www.scopus.com/inward/record.url?scp=85055729633&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2018.10.037

DO - 10.1016/j.aim.2018.10.037

M3 - Article (Academic Journal)

AN - SCOPUS:85055729633

SN - 0001-8708

VL - 341

SP - 299

EP - 335

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Subconvexity for modular form L-functions in the t aspect

Abstract

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

Professor Andrew R Booker

Cite this

Subconvexity for modular form L-functions in the t aspect

Abstract

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

Profiles

Professor Andrew R Booker

Cite this