Double exponential sums with exponential functions

Igor E. Shparlinski; Kam Hung Yau

doi:10.1142/S179304211750141X

Double exponential sums with exponential functions

Igor E. Shparlinski^*, Kam Hung Yau

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We obtain several estimates for double rational exponential sums modulo a prime (Formula presented.) with products (Formula presented.) where both (Formula presented.) and (Formula presented.) run through short intervals and (Formula presented.) is fixed integer. We also obtain some new estimates for the number of points on exponential modular curves (Formula presented.) and similar.

Original language	English
Pages (from-to)	2531-2543
Number of pages	13
Journal	International Journal of Number Theory
Volume	13
Issue number	10
DOIs	https://doi.org/10.1142/S179304211750141X
Publication status	Published - 2017
Externally published	Yes

Keywords

cancellation
exponential function
Exponential sums
solutions to congruences in small boxes

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10.1142/S179304211750141X

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@article{48fec84e43d9456db4a4fdebf0d2f18e,

title = "Double exponential sums with exponential functions",

abstract = "We obtain several estimates for double rational exponential sums modulo a prime (Formula presented.) with products (Formula presented.) where both (Formula presented.) and (Formula presented.) run through short intervals and (Formula presented.) is fixed integer. We also obtain some new estimates for the number of points on exponential modular curves (Formula presented.) and similar.",

keywords = "cancellation, exponential function, Exponential sums, solutions to congruences in small boxes",

author = "Shparlinski, \{Igor E.\} and Yau, \{Kam Hung\}",

year = "2017",

doi = "10.1142/S179304211750141X",

language = "English",

volume = "13",

pages = "2531--2543",

journal = "International Journal of Number Theory",

issn = "1793-0421",

publisher = "World Scientific Publishing",

number = "10",

}

TY - JOUR

T1 - Double exponential sums with exponential functions

AU - Shparlinski, Igor E.

AU - Yau, Kam Hung

PY - 2017

Y1 - 2017

N2 - We obtain several estimates for double rational exponential sums modulo a prime (Formula presented.) with products (Formula presented.) where both (Formula presented.) and (Formula presented.) run through short intervals and (Formula presented.) is fixed integer. We also obtain some new estimates for the number of points on exponential modular curves (Formula presented.) and similar.

AB - We obtain several estimates for double rational exponential sums modulo a prime (Formula presented.) with products (Formula presented.) where both (Formula presented.) and (Formula presented.) run through short intervals and (Formula presented.) is fixed integer. We also obtain some new estimates for the number of points on exponential modular curves (Formula presented.) and similar.

KW - cancellation

KW - exponential function

KW - Exponential sums

KW - solutions to congruences in small boxes

UR - https://www.scopus.com/pages/publications/85020525357

U2 - 10.1142/S179304211750141X

DO - 10.1142/S179304211750141X

M3 - Article

AN - SCOPUS:85020525357

SN - 1793-0421

VL - 13

SP - 2531

EP - 2543

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 10

ER -

Double exponential sums with exponential functions

Abstract

Keywords

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