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Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/41607
Description: We show that the communication complexity of the parity of the sum of binary digits of x+y is at least 0.085667...n+O(1) where x and y are n-bit integers. We also obtain a nontrivial (but weaker) lowe ... More
Reviewed: Reviewed
Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/48143
Description: For a prime p, we obtain an upper bound on the discrepancy of fractions r/p, where r runs through all of roots modulo p of all monic univariate polynomials of degree d whose vector of coefficients bel ... More
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Reviewed: Reviewed
Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/25302
Description: We estimate exponential sums of the form [equation omitted for formatting reasons] where f is a polynomial with integer cofficients, and ind n is the discrete logarithm of n modulo an odd prime p and ... More
Reviewed: Reviewed
Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/81785
Description: We use character sums to confirm several recent conjectures of V. I. Arnold on the uniformity of distribution properties of a certain dynamical system in a finite field. On the other hand, we show tha ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/43466
Description: Given an integer n, how hard is it to find the set of all integers m such that φ(m) = n, where φ is the Euler totient function? We present a certain basic algorithm which, given the prime number facto ... More
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Reviewed: Reviewed
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: journal article
Identifier: http://hdl.handle.net/1959.14/7831
Description: We obtain an upper bound on exponential sums of a new type with linear recurrence sequences. We apply this bound to estimate the Fourier coefficients, and thus the nonlinearity, of a Boolean function ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20160
Description: We use bounds of exponential sums to derive new lower bounds on the number of distinct distances between all pairs of points (x,y) ∈ A×B for two given sets A,B ∈ Fnq, where Fq is a finite field of q e ... More
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Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20159
Description: We study the sum [equation omitted for formating reasons] of consecutive iterations of the Euler function φ(n) (where the last iteration satisfies φ(k(n))(n) = 1). We show that for almost all n, the d ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20149
Description: We show that the fractional parts of the ratios n/ω(n), n/aω(n), n/τ(n) and n/aτ(n), where a ≥ 2 is a fixed integer and, as usual, ω(n) and τ(n) denote the number of prime divisors and the total numbe ... More
Reviewed: Reviewed
Date: 2005
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/81164
Description: 17 page(s)
Full Text: Full Text
Reviewed: Reviewed
Date: 2004
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/118615
Description: 19 page(s)
Reviewed: Reviewed
Date: 2004
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/118688
Description: We use lattice reduction to obtain a polynomial time algorithm for recovering an integer (up to a small interval) from its residues modulo sufficiently many primes, when the residues are corrupted by ... More
Reviewed: Reviewed
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