Congruences and exponential sums with the Euler function

WD Banks; Igor Shparlinski

Congruences and exponential sums with the Euler function

WD Banks^*, Igor Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

Abstract

We give upper bounds for the number of solutions to congruences with the Euler function phi(n) and with the Carmichael function lambda(n). We also give nontrivial bounds for certain exponential sums involving phi(n). Analogous results can also be obtained for the sum of divisors function and similar arithmetic functions.

Original language	English
Title of host publication	High primes and misdemeanours
Subtitle of host publication	lectures in honour of the 60th birthday of Hugh Cowie Williams
Editors	A VanDerPoorten, A Stein
Place of Publication	Providence
Publisher	American Mathematical Society
Pages	49-59
Number of pages	11
ISBN (Print)	0821833537
Publication status	Published - 2004
Event	International Conference in Number Theory in Honour of Hugh Williams on his 60th Birthday - Banff, Alberta, Canada Duration: 24 May 2003 → 30 May 2003

Publication series

Name	FIELDS INSTITUTE COMMUNICATIONS
Publisher	AMER MATHEMATICAL SOC
Volume	41

Conference

Conference	International Conference in Number Theory in Honour of Hugh Williams on his 60th Birthday
Country/Territory	Canada
City	Banff, Alberta
Period	24/05/03 → 30/05/03

Cite this

@inproceedings{e9df8a04e57640b7ad4bdea995d7dfeb,

title = "Congruences and exponential sums with the Euler function",

abstract = "We give upper bounds for the number of solutions to congruences with the Euler function phi(n) and with the Carmichael function lambda(n). We also give nontrivial bounds for certain exponential sums involving phi(n). Analogous results can also be obtained for the sum of divisors function and similar arithmetic functions.",

author = "WD Banks and Igor Shparlinski",

year = "2004",

language = "English",

isbn = "0821833537",

series = "FIELDS INSTITUTE COMMUNICATIONS",

publisher = "American Mathematical Society",

pages = "49--59",

editor = "A VanDerPoorten and A Stein",

booktitle = "High primes and misdemeanours",

address = "United States",

note = "International Conference in Number Theory in Honour of Hugh Williams on his 60th Birthday ; Conference date: 24-05-2003 Through 30-05-2003",

}

Banks, WD & Shparlinski, I 2004, Congruences and exponential sums with the Euler function. in A VanDerPoorten & A Stein (eds), High primes and misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams. FIELDS INSTITUTE COMMUNICATIONS, vol. 41, American Mathematical Society, Providence, pp. 49-59, International Conference in Number Theory in Honour of Hugh Williams on his 60th Birthday, Banff, Alberta, Canada, 24/05/03.

Congruences and exponential sums with the Euler function. / Banks, WD; Shparlinski, Igor.
High primes and misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams. ed. / A VanDerPoorten; A Stein. Providence: American Mathematical Society, 2004. p. 49-59 (FIELDS INSTITUTE COMMUNICATIONS; Vol. 41).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

TY - GEN

T1 - Congruences and exponential sums with the Euler function

AU - Banks, WD

AU - Shparlinski, Igor

PY - 2004

Y1 - 2004

N2 - We give upper bounds for the number of solutions to congruences with the Euler function phi(n) and with the Carmichael function lambda(n). We also give nontrivial bounds for certain exponential sums involving phi(n). Analogous results can also be obtained for the sum of divisors function and similar arithmetic functions.

AB - We give upper bounds for the number of solutions to congruences with the Euler function phi(n) and with the Carmichael function lambda(n). We also give nontrivial bounds for certain exponential sums involving phi(n). Analogous results can also be obtained for the sum of divisors function and similar arithmetic functions.

M3 - Conference proceeding contribution

SN - 0821833537

T3 - FIELDS INSTITUTE COMMUNICATIONS

SP - 49

EP - 59

BT - High primes and misdemeanours

A2 - VanDerPoorten, A

A2 - Stein, A

PB - American Mathematical Society

CY - Providence

T2 - International Conference in Number Theory in Honour of Hugh Williams on his 60th Birthday

Y2 - 24 May 2003 through 30 May 2003

ER -

Congruences and exponential sums with the Euler function

Abstract

Publication series

Conference

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