相关论文: On the Cycle Structure of Repeated Exponentiation …
Given a number $r$, we consider the dynamical system generated by repeated exponentiations modulo $r$, that is, by the map $u \mapsto f_g(u)$, where $f_g(u) \equiv g^u \pmod r$ and $0 \le f_g(u) \le r-1$. The number of cycles of the defined…
Given a prime $p$, we consider the dynamical system generated by repeated exponentiations modulo $p$, that is, by the map $u \mapsto f_g(u)$, where $f_g(u) \equiv g^u \pmod p$ and $0 \le f_g(u) \le p-1$. This map is in particular used in a…
We prove a recursive formula for the exterior and symmetric powers of modules for a cyclic 2-group. This makes computation straightforward. Previously, a complete description was only known for cyclic groups of prime order.
We study the algebraic dynamical systems generated by triangular systems of rational functions and estimate the height growth of iterations generated by such systems. Further, using a result on the reduction modulo primes of systems of…
We consider the reduction of an elliptic curve defined over the rational numbers modulo primes in a given arithmetic progression and investigate how often the subgroup of rational points of this reduced curve is cyclic as a special case of…
Explicit formulas are obtained for the number of periodic points and maximum tail length of split polynomial maps over finite fields for affine and projective space. This work includes a detailed analysis of the structure of the directed…
We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra.…
In this article, we study the cyclicity problem of elliptic curves $E/\Bbb{Q}$ modulo primes in a given arithmetic progression. We extend the recent work of Akbal and G\"ulo\u{g}lu by proving an unconditional asymptotic for such a cyclicity…
In 2004 Vasiga and Shallit studied the number of periodic points of two particular discrete quadratic maps modulo prime numbers. They found the asymptotic behaviour of the sum of the number of periodic points for all primes less than some…
New exceptional (i.e. non-repeating) prime number multiplets are given and formulated in terms of arithmetic progressions, along with laws governing them. Accompanying repeating prime number multiplets are pointed out. Prime number…
Two distinct systems of commutative complex numbers in n dimensions are described, of polar and planar types. Exponential forms of n-complex numbers are given in each case, which depend on geometric variables. Azimuthal angles, which are…
We study tensor powers of rank 1 sign-normalized Drinfeld A-modules, where A is the coordinate ring of an elliptic curve over a finite field. Using the theory of A-motives, we find explicit formulas for the A-action of these modules. Then,…
This work is meant to demonstrate new class of prime numbers -- cyclic prime numbers, that can be derived from any prime number at certain numeric systems. Cyclic prime numbers are also related to the cyclic numbers and full reptend prime…
In this paper we shall investigate the problem of the representation of the number of integral points of an elliptic curve modulo a prime number p. We present a way of expressing an exponential sum which involves polynomials of third…
This paper is a study of power series, where the coefficients are binomial expressions (iterated finite differences). Our results can be used for series summation, for series transformation, or for asymptotic expansions involving Stirling…
We present an asymptotic evaluation unitary formula for large argument values existing for defined class of functions. The asymptotic evaluation is obtained using only power series expansion coefficients of a function, what is a new result…
Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asymptotic values for the coefficients even for very small values…
The theta cycle of a modular form modulo a prime $p\geq 5$ is well understood. By contrast, the theta cycle modulo a power of $p$ is still mysterious and experimentally erratic. Here we completely determine the theta cycle of a weight $k <…
Combinatorial formulas expressing cyclic rook polynomials and cyclic permanents of rectangular matrices in terms of expansions along rows are presented
We describe iterated integrals as unipotent periods on families of marked elliptic curves in terms of multiple zeta values and elliptic multiple zeta values.