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Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195166
Description: We consider various counting questions for irreducible binomials of the form Xt-a over finite fields. We use various results from analytic number theory to investigate these questions.
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: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195172
Description: We establish new results about the frequency of small gaps between the elements of multiplicative subgroups of finite fields. As an application, we give some rigorous support to uniqueness assumptions ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1235134
Description: For a large prime p, and a polynomial ƒ over a finite field double-struck Fp of p elements, we obtain a lower bound on the size of the multiplicative subgroup of double-struck Fp∗ containing H ≥ 1 con ... 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/1959.14/1195893
Description: 13 page(s)
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: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/129331
Description: We obtain a lower bound on the multiplicative order of Gauss periods which generate normal bases over finite fields. This bound improves the previous bound of von zur Gathen and Shparlinski.
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/128917
Description: We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets ... More
Reviewed: Reviewed
Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/25127
Description: We consider the problem of determining the period of a sequence over an unknown finite field, given a black-box which returns only a few most significant bits of the sequence elements. For sequences w ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.14/8814
Description: 19 page(s)
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
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.14/8207
Description: 37 page(s)
Date: 2004
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/78663
Description: 8 page(s)
Reviewed: Reviewed
Date: 2003
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/118610
Description: We solve two computational problems concerning plane algebraic curves over finite fields: generating a uniformly random point, and finding all points deterministically in amortized polynomial time (ov ... More
Full Text: Full Text
Reviewed: Reviewed
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