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Date: 2006
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20349
Description: We give upper bounds for the number of solutions to congruences with the Euler function ϕ(n) modulo an integer q ≥ 2. We also give nontrivial bounds for rational exponential sums with ϕ(n)/q.
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195192
Description: We derive two new upper bounds on the double multiplicative character sum over subgroups and intervals Rχ(a,g,I,N)=∑x=1H|∑n=1Nχ(x+agⁿ)| where χ is a multiplicative character modulo a prime p, H and N ... More
Reviewed: Reviewed
Date: 2011
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/157964
Description: 13 page(s)
Reviewed: Reviewed
Date: 2007
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1158958
Description: 14 page(s)
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195127
Description: 18 page(s)
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195180
Description: 10 page(s)
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/13401
Description: We obtain upper bounds on character sums and autocorrelation of nonlinear recurrence sequences over arbitrary finite rings.
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195084
Description: 13 page(s)
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/144773
Description: Given a prime p, the Fermat quotient qp(u) of u with gcd (u,p)=1 is defined by the conditions qp(u) ≡ up-1-1/p mod p, -< qp (u) ≤ p -1. We derive a new bound on multiplicative character sums with Ferm ... More
Full Text: Full Text
Reviewed: Reviewed
Date: 2006
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20133
Description: We estimate multiplicative character sums taken on the values of a nonhomogeneous Beatty sequence {⌊αn + β⌋ : n = 1, 2, . . . }, where α, β ∈ R, and α is irrational. In particular, our bounds imply th ... More
Reviewed: Reviewed
Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1142098
Description: Let χ be a primitive multiplicative character modulo an integer m ≥ 1. Using some classical bounds of character sums, we estimate the average value of the character sums with subsequence sums Tm (S,χ) ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20158
Description: We estimate certain double character sums over points of an elliptic curve and in the multiplicative subgroup of a finite field. These bounds both improve and extend the scope of a series of previous ... More
Reviewed: Reviewed
Date: 2006
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20094
Description: For a fixed integer s ≥ 1, we estimate exponential sums with harmonic sums [equation omitted for formatting reasons] individually and on average, where Hs (n) is computed modulo a prime p. These bound ... More
Reviewed: Reviewed
Date: 2011
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/140204
Description: J. Bourgain and the author have recently estimated exponential sums with consecutive modular roots θ1/n (mod p), where θ is of multiplicative order t ≥ pε modulo a prime p (for some fixed ε > 0) and n ... More
Reviewed: Reviewed
Date: 2006
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20134
Description: We give nontrivial bounds in various ranges for exponential sums of the form [equation omitted for formatting reasons] and [equation omitted for formatting reasons] where m ≥ 2, ϑ is an element of ord ... More
Reviewed: Reviewed