排序方式: 共有112条查询结果,搜索用时 125 毫秒
101.
Given two sets
A, B í \Bbb Fqd{\cal A}, {\cal B}\subseteq {\Bbb F}_q^d
, the set of d dimensional vectors over the finite field
\Bbb Fq{\Bbb F}_q
with q elements, we show that the sumset
A+B = {a+b | a ? A, b ? B}{\cal A}+{\cal B} = \{{\bf a}+{\bf b}\ \vert\ {\bf a} \in {\cal A}, {\bf b} \in {\cal B}\}
contains a geometric progression of length k of the form vΛ
j
, where j = 0,…, k − 1, with a nonzero vector
v ? \Bbb Fqd{\bf v} \in {\Bbb F}_q^d
and a nonsingular d × d matrix Λ whenever
# A # B 3 20 q2d-2/k\# {\cal A} \# {\cal B} \ge 20 q^{2d-2/k}
. We also consider some modifications of this problem including the question of the existence of elements of sumsets on algebraic
varieties. 相似文献
102.
Edwin D. El-Mahassni Igor E. Shparlinski Arne Winterhof 《Monatshefte für Mathematik》2006,148(4):297-307
The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom
number generation. In this paper we present a new bound on the s-dimensional discrepancy of nonlinear congruential pseudorandom numbers over the residue ring
modulo M for an “almost squarefree” integer M. It is useful to recall that almost all integers are of this type. Moreover, if the generator is associated with a permutation
polynomial over
we obtain a stronger bound “on average” over all initial values. This bound is new even in the case when M = p is prime. 相似文献
103.
We study some arithmetic properties of the Ramanujan function τ(n), such as the largest prime divisorP (τ(n)) and the number of distinct prime divisors ω (τ (n)) of τ(n) for various sequences ofn. In particular, we show thatP(τ(n)) ≥ (logn)33/31+o(1) for infinitely many n, and
for every primep with τ(ρ) ≠ 0.
Dedicated to T N Shorey on his sixtieth birthday 相似文献
104.
Igor E. Shparlinski 《Japanese Journal of Mathematics》2012,7(2):235-294
We give a survey of a variety of recent results about the distribution and some geometric properties of points (x, y) on modular hyperbolas ${xy \equiv a\;(\mod m)}$ . We also outline a very diverse range of applications of such results, discuss multivariate generalisations and suggest a number of open problems of different levels of difficulty. 相似文献
105.
We prove an asymptotic formula for the number of representations of an integer as sum of two Lehmer numbers which implies that under some natural restrictions each sufficiently large integer is a sum of two such numbers. 相似文献
106.
In a recent work, Shallit and Vasiga have obtained several results about tails and cycles in orbits of repeated squaring. Some of these results have been based on the Extended Riemann Hypothesis. Here, we extend their result to repeated exponentiation with any fixed exponent e and also show that in fact classical unconditional results about the distribution of primes in arithmetic progressions, combined with very elementary arguments, are quite sufficient to generalise and give an unconditional proof of their asymptotic formulas. 相似文献
107.
Igor E. Shparlinski 《Periodica Mathematica Hungarica》2013,67(1):55-61
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. This is a relaxed version of the still open question, studied by P. Erd?s, A. M. Odlyzko and A. Sárközy, that corresponds to k = 1 (that is, to products of two primes). 相似文献
108.
On Some Properties of the Shrinking Generator 总被引:1,自引:0,他引:1
Igor Shparlinski 《Designs, Codes and Cryptography》2001,23(2):147-156
We obtain several results about the output rate and distribution ofzeros and ones of the shrinking generator associated with two linear recurringsequences. These results are based on various bounds on the number of zeros of linearrecurring sequences. Non-linear recurring sequences are considered aswell. 相似文献
109.
We show that the elliptic curve analogue of the pseudo-random number function, introduced recently by M. Naor and O. Reingold, produces a sequence with large linear complexity. This result generalizes a similar result of F. Griffin and I. E. Shparlinski for the linear complexity of the original function of M. Naor and O. Reingold. The proof is based on some results about the distribution of subset-products in finite fields and some properties of division polynomials of elliptic curves. 相似文献
110.
Jaime Gutierrez Harald Niederreiter Igor E. Shparlinski 《Monatshefte für Mathematik》2000,129(1):31-36
The inversive congruential method is an attractive alternative to the classical linear congruential method for pseudorandom
number generation. In this paper we present the first nontrivial bounds on the multidimensional discrepancy of individual
sequences of inversive congruential pseudorandom numbers in parts of the period. The proof is based on a new bound for certain
incomplete exponential sums.
(Received 3 December 1998) 相似文献