Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms

Atul Dixit; Arindam Roy; Alexandru Zaharescu

doi:10.1016/j.jmaa.2015.01.066

Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms

Atul Dixit, Arindam Roy, Alexandru Zaharescu

Mathematics

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

Abstract

We generalize a result of Ramanujan, Hardy and Littlewood to the setting of primitive Hecke forms, which interestingly exhibits faster convergence than in the initial case of the Riemann zeta function. We also provide a criterion in the spirit of Riesz for the Riemann Hypothesis for the associated L-functions.

Original language	English (US)
Pages (from-to)	594-611
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	426
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2015.01.066
State	Published - Jun 1 2015

Keywords

Bessel function
Dirichlet series
Hecke form
Hypergeometric function
Möbius function
Ramanujan tau function

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1016/j.jmaa.2015.01.066

Library availability

Discover UIUC Full Text

Cite this

@article{1028826d6b9c4980986828f74c4da985,

title = "Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms",

abstract = "We generalize a result of Ramanujan, Hardy and Littlewood to the setting of primitive Hecke forms, which interestingly exhibits faster convergence than in the initial case of the Riemann zeta function. We also provide a criterion in the spirit of Riesz for the Riemann Hypothesis for the associated L-functions.",

keywords = "Bessel function, Dirichlet series, Hecke form, Hypergeometric function, M{\"o}bius function, Ramanujan tau function",

author = "Atul Dixit and Arindam Roy and Alexandru Zaharescu",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2015",

month = jun,

day = "1",

doi = "10.1016/j.jmaa.2015.01.066",

language = "English (US)",

volume = "426",

pages = "594--611",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms

AU - Dixit, Atul

AU - Roy, Arindam

AU - Zaharescu, Alexandru

PY - 2015/6/1

Y1 - 2015/6/1

N2 - We generalize a result of Ramanujan, Hardy and Littlewood to the setting of primitive Hecke forms, which interestingly exhibits faster convergence than in the initial case of the Riemann zeta function. We also provide a criterion in the spirit of Riesz for the Riemann Hypothesis for the associated L-functions.

AB - We generalize a result of Ramanujan, Hardy and Littlewood to the setting of primitive Hecke forms, which interestingly exhibits faster convergence than in the initial case of the Riemann zeta function. We also provide a criterion in the spirit of Riesz for the Riemann Hypothesis for the associated L-functions.

KW - Bessel function

KW - Dirichlet series

KW - Hecke form

KW - Hypergeometric function

KW - Möbius function

KW - Ramanujan tau function

UR - http://www.scopus.com/inward/record.url?scp=84922860436&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922860436&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2015.01.066

DO - 10.1016/j.jmaa.2015.01.066

M3 - Article

AN - SCOPUS:84922860436

SN - 0022-247X

VL - 426

SP - 594

EP - 611

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this