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Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195084
Description: 13 page(s)
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/1959.14/1193207
Description: We use character sums to derive new bounds on the additive energy of the set of distances (counted with multiplicities) between two subsets of a vector space over a given finite field. We also give ap ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195126
Description: 20 page(s)
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195152
Description: Given a prime ℓ ≥ 3 and a positive integer k ≤ ℓ −2, one can define a matrix Dk,ℓ, the so-called Demjanenko matrix, whose rank is equal to the dimension of the Hodge group of the Jacobian Jac(Ck,ℓ) of ... 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: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195147
Description: We show that for any ϵ > 0 and a sufficiently large cube-free q, any reduced residue class modulo q can be represented as a product of 14 integers from the interval [1, q1/4,e1/2 + ϵ]. The length of t ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1190193
Description: We obtain a new estimate, on average, over primes p in a dyadic interval, on the number of integers u, v of absolute value at most h which fall in a given multiplicative subgroup of the residue ring m ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1190171
Description: 8 page(s)
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197409
Description: We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upp ... 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/1959.14/1200563
Description: We obtain a new bound of certain double multiplicative character sums. We use this bound together with some other previously obtained results to obtain new algorithms for finding roots of polynomials ... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197318
Description: Given two sets A and B of integers, we consider the problem of finding a set S⊆A of the smallest possible cardinality such the greatest common divisor of the elements of S∪B equals that of those of A∪ ... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1201720
Description: We give deterministic polynomial time algorithms for two different decision version the modular inversion hidden number problem introduced by D. Boneh, S. Halevi and N. A. Howgrave-Graham in 2001. For ... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197426
Description: We obtain new results about the representation of almost all residues modulo a prime p by a product of a small integer and also an element of small multiplicative subgroup of (ℤ/pℤ)*. These results ar ... More
Reviewed: Reviewed