Shifted moments of l-functions and moments of theta functions

Marc Munsch

doi:10.1112/S0025579316000218

Shifted moments of l-functions and moments of theta functions

Marc Munsch^*

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

Assuming the Riemann Hypothesis, Soundararajan [Ann. of Math.a (2) 170 (2009), 981-993] showed that f^T₀ ℓ.1=2 C it/^2κ T .log T /^κk2+€ His method was used by Chandee [Q.A J. Math. 62 (2011), 545-572] to obtain upper bounds for shifted moments of the Riemann Zeta function. Building on these ideas of Chandee and Soundararajan, we obtain, conditionally, upper bounds for shifted moments of Dirichlet-functions which allow us to derive upper bounds for moments of theta functions.

Original language	English
Pages (from-to)	196-212
Number of pages	17
Journal	Mathematika
Volume	63
Issue number	1
DOIs	https://doi.org/10.1112/S0025579316000218
Publication status	Published - 2017

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1112/S0025579316000218

Cite this

@article{66b87739bfad4f4d918aa76a46bba0a1,

title = "Shifted moments of l-functions and moments of theta functions",

abstract = "Assuming the Riemann Hypothesis, Soundararajan [Ann. of Math.a (2) 170 (2009), 981-993] showed that fT0 ℓ.1=2 C it/2κ T .log T /κk2+€ His method was used by Chandee [Q.A J. Math. 62 (2011), 545-572] to obtain upper bounds for shifted moments of the Riemann Zeta function. Building on these ideas of Chandee and Soundararajan, we obtain, conditionally, upper bounds for shifted moments of Dirichlet-functions which allow us to derive upper bounds for moments of theta functions.",

author = "Marc Munsch",

year = "2017",

doi = "10.1112/S0025579316000218",

language = "English",

volume = "63",

pages = "196--212",

journal = "Mathematika",

issn = "0025-5793",

publisher = "University College London",

number = "1",

}

TY - JOUR

T1 - Shifted moments of l-functions and moments of theta functions

AU - Munsch, Marc

PY - 2017

Y1 - 2017

N2 - Assuming the Riemann Hypothesis, Soundararajan [Ann. of Math.a (2) 170 (2009), 981-993] showed that fT0 ℓ.1=2 C it/2κ T .log T /κk2+€ His method was used by Chandee [Q.A J. Math. 62 (2011), 545-572] to obtain upper bounds for shifted moments of the Riemann Zeta function. Building on these ideas of Chandee and Soundararajan, we obtain, conditionally, upper bounds for shifted moments of Dirichlet-functions which allow us to derive upper bounds for moments of theta functions.

AB - Assuming the Riemann Hypothesis, Soundararajan [Ann. of Math.a (2) 170 (2009), 981-993] showed that fT0 ℓ.1=2 C it/2κ T .log T /κk2+€ His method was used by Chandee [Q.A J. Math. 62 (2011), 545-572] to obtain upper bounds for shifted moments of the Riemann Zeta function. Building on these ideas of Chandee and Soundararajan, we obtain, conditionally, upper bounds for shifted moments of Dirichlet-functions which allow us to derive upper bounds for moments of theta functions.

UR - http://www.scopus.com/inward/record.url?scp=85020703737&partnerID=8YFLogxK

U2 - 10.1112/S0025579316000218

DO - 10.1112/S0025579316000218

M3 - Article

AN - SCOPUS:85020703737

SN - 0025-5793

VL - 63

SP - 196

EP - 212

JO - Mathematika

JF - Mathematika

IS - 1

ER -

Shifted moments of l-functions and moments of theta functions

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this