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**Date:** 2004
**Subject Keyword:**
080200 Computation Theory and Mathematics
| exponential sums
| character sums
| extremal problems
| graphs
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/80512
**Description:**
In 1989, F. R. K. Chung gave a construction for certain directed h-regular graphs of small diameter.Her construction is based on finite fields, and the upper bound on the diameter of these graphs is d
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**Full Text:**
**Reviewed:**
**Authors:**
Shparlinski, Igor E
**Date:** 2013
**Subject Keyword:**
080200 Computation Theory and Mathematics
**Language:** eng
**Resource Type:** book chapter
**Identifier:** http://hdl.handle.net/1959.14/224276
**Description:**
We present a collection of several natural questions about elliptic curves, mostly over finite fields, that have led to some interesting number theoretic questions and whose solutions require rather i
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**Date:** 2017
**Subject Keyword:**
Polynomial ring
| Romanoff's theorem
| Irreducible polynomial
| Multiplicative order
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/1197769
**Description:**
Given a polynomial g of positive degree over a finite field, we show that the proportion of polynomials of degree n, which can be written as h+gk, where h is an irreducible polynomial of degree n and
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**Reviewed:**
**Date:** 2001
**Language:** eng
**Resource Type:** book
**Identifier:** http://hdl.handle.net/1959.14/118544
**Description:**
398 page(s)
**Date:** 2006
**Subject Keyword:**
080200 Computation Theory and Mathematics
| circulant graphs
| graph isomorphism
| Ádám conjecture
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/9747
**Description:**
Given two k element subsets S,T ⊆ ℤ<sub>n</sub>, we give a quasi-linear algorithm to either find λ ∈ ℤ*<sub>n</sub> such that S = λT or prove that no such λ exists. This question is closely related to
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**Reviewed:**
**Date:** 2011
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/134834
**Description:**
Aigner has defined elite primes as primes p such that all but finitely many of Fermat numbers F(n) = 2²ⁿ + 1, n = 0, 1, 2..., are quadratic nonresidues modulo p. Since the sequence of Fermat numbers i
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**Reviewed:**
**Date:** 2011
**Subject Keyword:**
010100 Pure Mathematics
| Distribution in arithmetic progressions
| Polynomials over prime numbers
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/154328
**Description:**
30 page(s)
**Reviewed:**
**Date:** 2012
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/195607
**Description:**
We give upper and lower bounds on the count of positive integers n <= x dividing the nth term of a non-degenerate linearly recurrent sequence with simple roots.
**Full Text:**
**Reviewed:**
**Authors:**
Shparlinski, Igor E
**Date:** 2010
**Subject Keyword:**
010100 Pure Mathematics
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/119101
**Description:**
Let E/ℚ be a fixed elliptic curve over ℚ which does not have complex multiplication. Assuming the Generalized Riemann Hypothesis, Cojocaru and Duke have obtained an asymptotic formula for the number o
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**Reviewed:**
**Date:** 2009
**Subject Keyword:**
010100 Pure Mathematics
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/130445
**Description:**
25 page(s)
**Reviewed:**
**Authors:**
Shparlinski, Igor E
**Date:** 2013
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/272086
**Description:**
We show that the reductions modulo primes p ≤ x of the elliptic curve Ea,b : Y² = X³ + aX + b behave as predicted by the Sato-Tate conjecture, on average over integers a and b such that a ∈ A and b ∈
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**Reviewed:**
**Authors:**
Shparlinski, Igor E
**Date:** 2008
**Subject Keyword:**
010100 Pure Mathematics
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/78537
**Description:**
13 page(s)
**Reviewed:**
**Date:** 2010
**Subject Keyword:**
080200 Computation Theory and Mathematics
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/125235
**Description:**
In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degree growth of these iterations. We use these estimates to bound exponential
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**Reviewed:**
**Date:** 2010
**Subject Keyword:**
010100 Pure Mathematics
| multivariate polynomial
| pseudorandom number generator
| discrepancy
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/115255
**Description:**
We bound exponential sums along the orbits of essentially arbitrary multivariate polynomial dynamical systems, provided that the orbits are long enough. We use these bounds to derive nontrivial estima
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**Reviewed:**
**Date:** 2010
**Subject Keyword:**
010100 Pure Mathematics
| dynamical systems
| orbits
| exponential sums
| additive combinatorics
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/118625
**Description:**
8 page(s)
**Full Text:**
**Reviewed:**

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