Results 11 to 20 of about 1,276 (42)
On Some Dynamical Systems in Finite Fields and Residue Rings
, 2007 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 that some conjectures are wrong.
Shparlinski, Igor E.
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The Polyhedron-Hitting Problem [PDF]
, 2014 We consider polyhedral versions of Kannan and Lipton's Orbit Problem (STOC '80 and JACM '86)---determining whether a target polyhedron V may be reached from a starting point x under repeated applications of a linear transformation A in an ambient vector ...
Chonev, Ventsislav +2 more
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Artin's primitive root conjecture -a survey - [PDF]
, 2012 This is an expanded version of a write-up of a talk given in the fall of 2000 in Oberwolfach. A large part of it is intended to be understandable by non-number theorists with a mathematical background.
Moree, Pieter
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Prime Factors of Dynamical Sequences
, 2010 Let f(t) be a rational function of degree at least 2 with rational coefficients. For a given rational number x_0, define x_{n+1}=f(x_n) for each nonnegative integer n.
Faber, Xander, Granville, Andrew
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Distribution of Eigenvalues for the Modular Group [PDF]
, 1995 The two-point correlation function of energy levels for free motion on the modular domain, both with periodic and Dirichlet boundary conditions, are explicitly computed using a generalization of the Hardy-Littlewood method. It is shown that ion the limit
A. Selberg +36 more
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Exponential sums and polynomial congruences in two variables: the quasi-homogeneous case [PDF]
, 2012 We adapt ideas of Phong, Stein and Sturm and ideas of Ikromov and M\"uller from the continuous setting to various discrete settings, obtaining sharp bounds for exponential sums and the number of solutions to polynomial congruences for general quasi ...
Wright, James
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Lucas' theorem: its generalizations, extensions and applications (1878--2014) [PDF]
, 2014 In 1878 \'E. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient ${n\choose m}$ modulo a prime $p$ in terms of the binomial coefficients of the base-$p$ digits of $n$ and $m$: {\it If $p$ is a prime, $n=n_0 ...
Meštrović, Romeo
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Rigorous Analysis of a Randomised Number Field Sieve
, 2018 Factorisation of integers $n$ is of number theoretic and cryptographic significance. The Number Field Sieve (NFS) introduced circa 1990, is still the state of the art algorithm, but no rigorous proof that it halts or generates relationships is known.
Lee, Jonathan, Venkatesan, Ramarathnam
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The order of the reductions of an algebraic integer
, 2014 Let K be a number field, and let a be a non-zero element of K. Fix some prime number l. We compute the density of the following set: the primes p of K such that the multiplicative order of the reduction of a modulo p is coprime to l (or, more generally ...
Perucca, Antonella
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On the linear complexity of Sidel'nikov Sequences over Fd [PDF]
, 2006 We study the linear complexity of sequences over the prime field Fd introduced by Sidel’nikov. For several classes of period length we can show that these sequences have a large linear complexity.
Brandstätter, Nina, Meidl, Wilfried
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