๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the cycle structure of repeated exponentiation modulo a prime

โœ Scribed by Wun-Seng Chou; Igor E Shparlinski

Book ID
104024437
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
234 KB
Volume
107
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

The Commutant Modulo Cp of Co-prime Powe
The Commutant Modulo Cp of Co-prime Powers of Operators on a Hilbert Space
โœ B.P Duggal ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 114 KB

Let H be a separable infinite-dimensional complex Hilbert space and let A B โˆˆ B H , where B H is the algebra of operators on H into itself. Let ฮด A B B H โ†’ B H denote the generalized derivation ฮด AB X = AX -XB. This note considers the relationship between the commutant of an operator and the commuta