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Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221396
Description: 12 page(s)
Reviewed: Reviewed
Date: 2013
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/272190
Description: We obtain upper bounds on the number of solutions to congruences of the type (x1 + s)... (xv + s) ≡ (y1 + s)... (xv + s) ≢ 0 (mod p) modulo a prime p with variables from some short intervals. We give ... More
Reviewed: Reviewed
Date: 2013
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/279863
Description: 8 page(s)
Reviewed: Reviewed
Date: 2013
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/279792
Description: We consider a modification of the classical number theoretic question about the gaps between consecutive primitive roots modulo a prime p, which by the well-known result of Burgess are known to be at ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/276237
Description: The authors have recently introduced and studied a modification of the classical number theoretic question about the largest gap between consecutive quadratic non-residues and primitive roots modulo a ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/271249
Description: We show that for any integers a and m with m ≥ 1 and gcd(a,m) = 1, there is a solution to the congruence pr ≡ a (modm) where p is prime, r is a product of at most k = 17 prime factors and p, r ≤ m. Th ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/271283
Description: 11 page(s)
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/276005
Description: We obtain an asymptotic formula for the number of square-free integers in N consecutive values of polynomials on average over integral polynomials of degree at most k and of height at most H, where H ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221895
Description: 11 page(s)
Reviewed: Reviewed
Date: 2013
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221888
Description: 8 page(s)
Reviewed: Reviewed
Date: 2013
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/278983
Description: 15 page(s)
Reviewed: Reviewed
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 ∈ ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221657
Description: We improve an estimate of A. Granville (1987) on the number of vanishing Fermat quotients qp (ℓ) modulo a prime p when ℓ runs through primes ℓ ≤ N. We use this bound to obtain an unconditional improve ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221582
Description: 32 page(s)
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/272100
Description: We present some theoretical bounds and algorithms concerning the statistics of different reduction types in the family of Fermat curves Yp = Xs(1 - X ), where p is prime and s = 1,..., p - 2.
Reviewed: Reviewed