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Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/81785
Description: We use character sums to confirm several recent conjectures of V. I. Arnold on the uniformity of distribution properties of a certain dynamical system in a finite field. On the other hand, we show tha ... More
Reviewed: Reviewed
Date: 2004
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/1229594
Description: For a system of polynomial equations over Qp we present an efficient construction of a single polynomial of quite small degree whose zero set over Qp coincides with, the zero set over Qp of the origin ... More
Reviewed: Reviewed
Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1142073
Description: Given two sets A, B ⊆ Fq d, the set of d dimensional vectors over the finite field q with q elements, we show that the sumset A+B = {a + b | a ∈ A, b ∈ B} contains a geometric progression of length k ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1194586
Description: We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithm ... More
Reviewed: Reviewed
Date: 2007
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1159038
Description: 15 page(s)
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/173573
Description: We estimate multiplicative character sums over the integers with a fixed sum of binary digits and apply these results to study the distribution of products of such integers in residues modulo a prime ... More
Reviewed: Reviewed
Date: 2009
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/130411
Description: 6 page(s)
Reviewed: Reviewed
Date: 2008
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/320509
Description: 7 page(s)
Reviewed: Reviewed
Date: 2010
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/128910
Description: 10 page(s)
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197903
Description: We obtain new bounds of multivariate exponential sums with monomials, when the variables run over rather short intervals. Furthermore, we use the same method to derive estimates on similar sums with m ... More
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/130997
Description: We give upper bounds for sums of multiplicative characters modulo an integer q ≧ 2 with the Euler function ϕ ( n ) and with the shifted largest prime divisor P ( n ) + a of integers n ≦ x .
Reviewed: Reviewed
Date: 2007
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/43395
Description: For a prime p and integers a and b, we consider Salié sums [equation omitted for formatting reasons] where χ2(x) is a quadratic character and x¯ is the modular inversion of x, that is, xx¯≡ 1 (mod p). ... More
Full Text: Full Text
Reviewed: Reviewed
Date: 2005
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.14/118651
Description: We give a survey of recent results on the hidden number problem introduced by Boneh and Venkatesan in 1996 and its numerous generalizations. Many of the results in this area are based on a rather surp ... More
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/271283
Description: 11 page(s)
Reviewed: Reviewed
Date: 2008
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/319709
Description: We obtain a new lower bound on the number of prime divisors of integers whose g-ary expansion contains a fixed number of nonzero digits.
Reviewed: Reviewed