scholarly journals The Diophantine problem for rings of exponential polynomials

2021 ◽  
pp. 8
Author(s):  
Dimitra Chompitaki ◽  
Natalia Garcia-Fritz ◽  
Hector Pasten ◽  
Thanases Pheidas ◽  
Xavier Vidaux
Keyword(s):  
Exponential Polynomials ◽  
Diophantine Problem

scholarly journals An Algebraic Criterion of Zero Solutions of Some Dynamic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Ying Wang ◽  
Baodong Zheng ◽  
Chunrui Zhang
Keyword(s):  
Dynamic Systems ◽  
Real Coefficient ◽  
Coupled Systems ◽  
Decomposition Technique ◽  
Exponential Polynomials ◽  
Basic Theorem ◽  
Algebraic Criterion ◽  
The Stability

We establish some algebraic results on the zeros of some exponential polynomials and a real coefficient polynomial. Based on the basic theorem, we develop a decomposition technique to investigate the stability of two coupled systems and their discrete versions, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts and the moduli of all roots of a real coefficient polynomial are less than 1.

scholarly journals On similarities between exponential polynomials and Hermite polynomials

2013 ◽  
Vol 12 (3) ◽  
pp. 93-104 ◽  
Author(s):  
Edyta Hetmaniok ◽  
◽  
Mariusz Pleszczynski ◽  
Damian Slota ◽  
Roman Witula ◽  
...  
Keyword(s):  
Hermite Polynomials ◽  
Exponential Polynomials

scholarly journals A diophantine problem on groups IV

1974 ◽  
Vol 18 (4) ◽  
pp. 552-564 ◽  
Author(s):  
R. C. Baker
Keyword(s):  
Diophantine Problem

Divisor Sums of Generalised Exponential Polynomials

1996 ◽  
Vol 39 (1) ◽  
pp. 35-46 ◽  
Author(s):  
G. R. Everest ◽  
I. E. Shparlinski
Keyword(s):  
Prime Ideal ◽  
Algebraic Integer ◽  
Linear Recurrence ◽  
Exponential Polynomial ◽  
Exponential Polynomials ◽  
Recurrence Sequence ◽  
Special Cases ◽  
Divisor Sums ◽  
Recurrence Sequences

AbstractA study is made of sums of reciprocal norms of integral and prime ideal divisors of algebraic integer values of a generalised exponential polynomial. This includes the important special cases of linear recurrence sequences and general sums of S-units. In the case of an integral binary recurrence sequence, similar (but stronger) results were obtained by P. Erdős, P. Kiss and C. Pomerance.

Bell–Sheffer exponential polynomials of the second kind

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Pierpaolo Natalini ◽  
Paolo Emilio Ricci
Keyword(s):  
Higher Order ◽  
Bell Numbers ◽  
Integer Sequences ◽  
Exponential Polynomials ◽  
Sheffer Polynomials

AbstractIn recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers and several integer sequences related to them have been studied. In the present paper, new sets of Bell–Sheffer polynomials are introduced. Connections with Bell numbers are shown.

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