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Date: 2017
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 ... More
Reviewed: Reviewed
Date: 2017
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197725
Description: 20 page(s)
Reviewed: Reviewed
Date: 2017
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1193205
Description: 8 page(s)
Reviewed: Reviewed
Date: 2016
Subject Keyword: Piatetski-Shapiro sequences | primes
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195062
Description: Let ℙc=(⌊pc⌋)p∈ℙ with c>1 and c∉ℕ, where ℙ is the set of prime numbers, and ⌊.⌋ is the floor function. We show that for every such c there are infinitely many members of ℙc having at most R(c) prime f ... More
Reviewed: Reviewed
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/1959.14/1195180
Description: 10 page(s)
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195121
Description: There is a well-known asymptotic formula, due to W. M. Schmidt [Duke Math. J., 35 (1968), pp. 327-339], for the number of full-rank integer lattices of index at most V in ℤⁿ. This set of lattices L ca ... More
Reviewed: Reviewed
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/1959.14/1195102
Description: We improve several recent results by Hong, Lee, Lee and Park (2012) on gaps and Bzdȩga (2014) on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvements, we also introduc ... More
Reviewed: Reviewed
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/1959.14/1055140
Description: Given a function f in a finite field Fq of q elements, we define the functional graph of f as a directed graph on q nodes labelled by the elements of Fq where there is an edge from u to v if and only ... 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: 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: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195127
Description: 18 page(s)
Reviewed: Reviewed