The distributioin of patterns of inverse modulo a prime

C. I. Cobeli; S. M. Gonek; A. Zaharescu

doi:10.1016/S0022-314X(03)00059-3

The distributioin of patterns of inverse modulo a prime

C. I. Cobeli, S. M. Gonek, A. Zaharescu

Mathematics

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

Abstract

We investigate the distribution of the numbers x ∈ [1,p] for which a₁x+b₁,...,a_sx + b_s (mod p) all lie in a subset N = {ν (mod p): M < ν ≤ M + N} of the set of multiplicative inverses modulo a prime p. Here the a_i are integers coprime to p and the numbers ā₁b₁,...,ā_sb_s are distinct (mod p).

Original language	English (US)
Pages (from-to)	209-222
Number of pages	14
Journal	Journal of Number Theory
Volume	101
Issue number	2
DOIs	https://doi.org/10.1016/S0022-314X(03)00059-3
State	Published - Aug 1 2003

Keywords

Distribution of mod p
Kloosterman sums
Patterns of inverse

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1016/S0022-314X(03)00059-3

Library availability

Discover UIUC Full Text

Cite this

@article{8ca98f8c76b0497fb31bdc845d29c235,

title = "The distributioin of patterns of inverse modulo a prime",

abstract = "We investigate the distribution of the numbers x ∈ [1,p] for which a1x+b1,...,asx + bs (mod p) all lie in a subset N = {ν (mod p): M < ν ≤ M + N} of the set of multiplicative inverses modulo a prime p. Here the ai are integers coprime to p and the numbers ā1b1,...,āsbs are distinct (mod p).",

keywords = "Distribution of mod p, Kloosterman sums, Patterns of inverse",

author = "Cobeli, {C. I.} and Gonek, {S. M.} and A. Zaharescu",

year = "2003",

month = aug,

day = "1",

doi = "10.1016/S0022-314X(03)00059-3",

language = "English (US)",

volume = "101",

pages = "209--222",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - The distributioin of patterns of inverse modulo a prime

AU - Cobeli, C. I.

AU - Gonek, S. M.

AU - Zaharescu, A.

PY - 2003/8/1

Y1 - 2003/8/1

N2 - We investigate the distribution of the numbers x ∈ [1,p] for which a1x+b1,...,asx + bs (mod p) all lie in a subset N = {ν (mod p): M < ν ≤ M + N} of the set of multiplicative inverses modulo a prime p. Here the ai are integers coprime to p and the numbers ā1b1,...,āsbs are distinct (mod p).

AB - We investigate the distribution of the numbers x ∈ [1,p] for which a1x+b1,...,asx + bs (mod p) all lie in a subset N = {ν (mod p): M < ν ≤ M + N} of the set of multiplicative inverses modulo a prime p. Here the ai are integers coprime to p and the numbers ā1b1,...,āsbs are distinct (mod p).

KW - Distribution of mod p

KW - Kloosterman sums

KW - Patterns of inverse

UR - http://www.scopus.com/inward/record.url?scp=0042205351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042205351&partnerID=8YFLogxK

U2 - 10.1016/S0022-314X(03)00059-3

DO - 10.1016/S0022-314X(03)00059-3

M3 - Article

AN - SCOPUS:0042205351

SN - 0022-314X

VL - 101

SP - 209

EP - 222

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 2

ER -

The distributioin of patterns of inverse modulo a prime

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this