Bounds for theta sums in higher rank. II

Jens Marklof; Matthew C Welsh

doi:10.1007/s11854-023-0333-9

Bounds for theta sums in higher rank. II

Jens Marklof^*, Matthew C Welsh

^*Corresponding author for this work

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

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Abstract

In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a linear term in the exponent, the estimates can be further improved for almost all parameter values. Our results extend the bound for one-variable theta sums obtained by Fedotov and Klopp in 2012.

Original language	English
Pages (from-to)	235–264
Journal	Journal d'Analyse Mathématique
Volume	151
DOIs	https://doi.org/10.1007/s11854-023-0333-9
Publication status	Published - 22 Dec 2023

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@article{8800d62d64284feba9e2327001cd0568,

title = "Bounds for theta sums in higher rank. II",

abstract = "In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a linear term in the exponent, the estimates can be further improved for almost all parameter values. Our results extend the bound for one-variable theta sums obtained by Fedotov and Klopp in 2012.",

author = "Jens Marklof and Welsh, \{Matthew C\}",

year = "2023",

month = dec,

day = "22",

doi = "10.1007/s11854-023-0333-9",

language = "English",

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journal = "Journal d'Analyse Math{\'e}matique",

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TY - JOUR

T1 - Bounds for theta sums in higher rank. II

AU - Marklof, Jens

AU - Welsh, Matthew C

PY - 2023/12/22

Y1 - 2023/12/22

N2 - In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a linear term in the exponent, the estimates can be further improved for almost all parameter values. Our results extend the bound for one-variable theta sums obtained by Fedotov and Klopp in 2012.

AB - In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a linear term in the exponent, the estimates can be further improved for almost all parameter values. Our results extend the bound for one-variable theta sums obtained by Fedotov and Klopp in 2012.

U2 - 10.1007/s11854-023-0333-9

DO - 10.1007/s11854-023-0333-9

M3 - Article (Academic Journal)

SN - 0021-7670

VL - 151

SP - 235

EP - 264

JO - Journal d'Analyse Mathématique

JF - Journal d'Analyse Mathématique

ER -

Bounds for theta sums in higher rank. II

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