Results 21 to 30 of about 312 (174)

Exponential Diophantine equations for correlation functions of the Tchebyscheff maps

四川大学学报. 自然科学版, 2023
Tchebyscheff maps are typical chaotic maps. Correlation functions play a key role in the study of their statistical properties. This paper aims at the solutions of a class of exponential Diophantine equations arising in the calculation of correlation ...
ZHOU Xing-Wang
doaj  

A Hasse-type principle for exponential Diophantine equations and its applications [PDF]

, 2016
We propose a conjecture, similar to Skolem's conjecture, on a Hasse-type principle for exponential Diophantine equations. We prove that in a sense the principle is valid for "almost all" equations.
Hajdu, Lajos, Bertók, Csanád
core   +1 more source

Heights and multiplicative relations on algebraic varieties [PDF]

, 2007
Points on a subvariety X of a semi-abelian variety A that are contained in a subgroup, let the subgroup be of finite rank or algebraic, are subject to severe restrictions arithmetical nature. Finiteness results for intersections of X with subgroups of
Habegger, Philipp
core   +1 more source

Exponential diophantine equations in rings of positive characteristic [PDF]

Journal of Knot Theory and Its Ramifications, 2020
In this paper, we prove an algorithmical solvability of exponential-Diophantine equations in rings represented by matrices over fields of positive characteristic. Consider the system of exponential-Diophantine equations [Formula: see text] where [Formula: see text] are constants from matrix ring of characteristic [Formula: see text], [Formula: see ...
Chilikov, A. A., Belov-Kanel, Alexey
openaire   +1 more source

A number theoretic method for high order correlations of the Ulam map

四川大学学报. 自然科学版, 2020
In this paper, a number theoretic method is introduced to calculate the high order correlation functions of the Ulam map. In this method, the calculation is firstly transformed into solving a class of exponential Diophantine equations with variable ...
Zhou Xing-Wang
doaj  

Linear forms in logarithms and exponential Diophantine equations

, 2020
This paper aims to show two things. Firstly the importance of Alan Baker's work on linear forms in logarithms for the development of the theory of exponential Diophantine equations.
Rob Tijdeman, Tijdeman, Rob
core   +1 more source

Diophantine equations after Fermat’s last theorem [PDF]

, 2009
The author considers the following two questions: {\parindent=7mm \item{(i)}Given a Diophantine equation, what information can be obtained by following the strategy of Wiles' proof of Fermat's last theorem?
Siksek, Samir, Samir Siksek
core   +1 more source

On a conjecture on exponential Diophantine equations [PDF]

Acta Arithmetica, 2009
We study the solutions of a Diophantine equation of the form $a^x+b^y=c^z$, where $a\equiv 2 \pmod 4$, $b\equiv 3 \pmod 4$ and $\gcd (a,b,c)=1$. The main result is that if there exists a solution $(x,y,z)=(2,2,r)$ with $r>1$ odd then this is the only solution in integers greater than 1, with the possible exception of finitely many values $(c,r)$. We
Cipu, Mihai, Mignotte, Maurice
openaire   +2 more sources

Formalizing a Diophantine Representation of the Set of Prime Numbers [PDF]

, 2022
The DPRM (Davis-Putnam-Robinson-Matiyasevich) theorem is the main step in the negative resolution of Hilbert’s 10th problem. Almost three decades of work on the problem have resulted in several equally surprising results.
Kaliszyk, Cezary, Pąk, Karol
core   +1 more source

Moderate Deviation Principles for Lacunary Trigonometric Sums

Mathematische Nachrichten, Volume 299, Issue 5, Page 1028-1044, May 2026.
ABSTRACT Classical works of Kac, Salem, and Zygmund, and Erdős and Gál have shown that lacunary trigonometric sums despite their dependency structure behave in various ways like sums of independent and identically distributed random variables. For instance, they satisfy a central limit theorem (CLT) and a law of the iterated logarithm.
Joscha Prochno, Marta Strzelecka
wiley   +1 more source