Upper and Lower Bounds for Higher Moments of Theta Functions

Marc Munsch; Igor E. Shparlinski

doi:10.1093/qmath/hav039

Upper and Lower Bounds for Higher Moments of Theta Functions

Marc Munsch, Igor E. Shparlinski^*

^*Corresponding author for this work

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

Abstract

We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of character sums and, in particular, on a modification of some recent results of M. Z. Garaev.

Original language	English
Pages (from-to)	53-73
Number of pages	21
Journal	The Quarterly Journal of Mathematics
Volume	67
Issue number	1
DOIs	https://doi.org/10.1093/qmath/hav039
Publication status	Published - 8 Dec 2014
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1093/qmath/hav039

Cite this

@article{41630600c4584b10bc693c745a831419,

title = "Upper and Lower Bounds for Higher Moments of Theta Functions",

abstract = "We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of character sums and, in particular, on a modification of some recent results of M. Z. Garaev.",

author = "Marc Munsch and Shparlinski, {Igor E.}",

year = "2014",

month = dec,

day = "8",

doi = "10.1093/qmath/hav039",

language = "English",

volume = "67",

pages = "53--73",

journal = "The Quarterly Journal of Mathematics",

issn = "0033-5606",

publisher = "Oxford University Press",

number = "1",

}

TY - JOUR

T1 - Upper and Lower Bounds for Higher Moments of Theta Functions

AU - Munsch, Marc

AU - Shparlinski, Igor E.

PY - 2014/12/8

Y1 - 2014/12/8

N2 - We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of character sums and, in particular, on a modification of some recent results of M. Z. Garaev.

AB - We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of character sums and, in particular, on a modification of some recent results of M. Z. Garaev.

UR - http://www.scopus.com/inward/record.url?scp=84962592809&partnerID=8YFLogxK

U2 - 10.1093/qmath/hav039

DO - 10.1093/qmath/hav039

M3 - Article

AN - SCOPUS:84962592809

SN - 0033-5606

VL - 67

SP - 53

EP - 73

JO - The Quarterly Journal of Mathematics

JF - The Quarterly Journal of Mathematics

IS - 1

ER -

Upper and Lower Bounds for Higher Moments of Theta Functions

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this