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Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197846
Description: Using a recent improvement by Bettin and Chandee to a bound of Duke, Friedlander and Iwaniec (1997) on double exponential sums with Kloosterman fractions, we establish a uniformity of distribution res ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195130
Description: We use new bounds of double exponential sums with ratios of integers from prescribed intervals to get an asymptotic formula for the number of solutions to congruences [equation presented here], with v ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197843
Description: We use the theory of exponent pairs and Vaaler polynomials to show that any interval of the form [x,x+x¹/²] contains an integral multiple m²r ∈ [x,x+x¹/²] of a perfect square m² with an integer m > x⁰ ... 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: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/332390
Description: 10 page(s)
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/271249
Description: We show that for any integers a and m with m ≥ 1 and gcd(a,m) = 1, there is a solution to the congruence pr ≡ a (modm) where p is prime, r is a product of at most k = 17 prime factors and p, r ≤ m. Th ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/181747
Description: 13 page(s)
Full Text: Full Text
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/202794
Description: We give a survey of a variety of recent results about the distribution and some geometric properties of points (x, y) on modular hyperbolas xy ≡ a (mod m). We also outline a very diverse range of appl ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/118625
Description: 8 page(s)
Full Text: Full Text
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/130407
Description: Given two relatively prime positive integers m < n we consider the smallest positive solution (x0, y0) to the equation mx - ny = 1. E. I. Dinaburg and Y. G. Sinai have used continued fractions to show ... More
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/130400
Description: Published Online First on 09 June 2009. We prove an asymptotic formula for the number of representations of an integer as sum of two Lehmer numbers which implies that under some natural restrictions e ... More
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/133006
Description: We show how to accelerate the subset sum pseudorandom number generator with arbitrary weights. Some special choices of weights speed up the naive usage of this generator without losing the property of ... More
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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
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/9952
Description: The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. In this paper we present a new bound on the s-dimensional ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/7826
Description: We give new bounds of exponential sums with sequences of iterations of Dickson polynomials over prime finite fields. This result is motivated by possible applications to polynomial generators of pseud ... More
Reviewed: Reviewed