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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: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1190162
Description: Given a finite field of Fq elements, we consider a trajectory of the map u→ f(u) associated with a polynomial f ∈ Fq[X]. Using bounds of character sums, under some mild condition on f, we show that fo ... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197784
Description: We introduce and use some new arguments to improve upper bounds of Chung and of Lu, Wan, Wang, and Zhang on the diameter of some Cayley graphs constructed from polynomials over a finite field.
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1201756
Description: We use the Burgess bound and combinatorial sieve to obtain an upper bound on the number of primes p in a dyadic interval [Q, 2Q] for which a given interval [u + 1, u + ψ(Q)] does not contain a quadrat ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195029
Description: 7 page(s)
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: 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: 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
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Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/159886
Description: 9 page(s)
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/119092
Description: Let E be an ordinary elliptic curve over a finite field Fq of q elements. We improve a bound on bilinear additive character sums over points on E, and obtain its analogue for bilinear multiplicative c ... More
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Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/128904
Description: 9 page(s)
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: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/129931
Description: 10 page(s)
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.14/118660
Description: Introduced by Kraitchik and Lehmer, an x-pseudosquare is a positive integer n ≡ I (mod 8) that is a quadratic residue for each odd prime p ≤ x, yet is not a square. We use bounds of character sums to ... More