scholarly journals ON THE SKOLEM PROBLEM AND SOME RELATED QUESTIONS FOR PARAMETRIC FAMILIES OF LINEAR RECURRENCE SEQUENCES

2021 ◽  
pp. 1-24 ◽  
Author(s):  
ALINA OSTAFE ◽  
IGOR E. SHPARLINSKI
Keyword(s):  
Linear Recurrence ◽  
Parametric Families ◽  
Recurrence Sequences

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.

scholarly journals Decomposable polynomials in second order linear recurrence sequences

2018 ◽  
Vol 159 (3-4) ◽  
pp. 321-346 ◽  
Author(s):  
Clemens Fuchs ◽  
Christina Karolus ◽  
Dijana Kreso
Keyword(s):  
Second Order ◽  
Linear Recurrence ◽  
Order Linear ◽  
Recurrence Sequences

scholarly journals Linear combinations of prime powers in binary recurrence sequences

2017 ◽  
Vol 13 (02) ◽  
pp. 261-271 ◽  
Author(s):  
Csanád Bertók ◽  
Lajos Hajdu ◽  
István Pink ◽  
Zsolt Rábai
Keyword(s):  
Linear Combination ◽  
The Other ◽  
Linear Recurrence ◽  
Linear Combinations ◽  
Other Hand ◽  
Sums Of Powers ◽  
Recurrence Sequences

We give finiteness results concerning terms of linear recurrence sequences having a representation as a linear combination, with fixed coefficients, of powers of fixed primes. On one hand, under certain conditions, we give effective bounds for the terms of binary recurrence sequences with such a representation. On the other hand, in the case of some special binary recurrence sequences, all terms having a representation as sums of powers of [Formula: see text] and [Formula: see text] are explicitly determined.

scholarly journals ‐PARTS OF TERMS OF INTEGER LINEAR RECURRENCE SEQUENCES

Mathematika ◽  
2017 ◽  
Vol 63 (3) ◽  
pp. 840-851
Author(s):  
Yann Bugeaud ◽  
Jan‐Hendrik Evertse
Keyword(s):  
Linear Recurrence ◽  
Recurrence Sequences

scholarly journals General Linear Recurrence Sequences and Their Convolution Formulas

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 132 ◽  
Author(s):  
Paolo Emilio Ricci ◽  
Pierpaolo Natalini
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Second Order ◽  
General Linear ◽  
Linear Recurrence ◽  
Order Linear ◽  
Matrix Polynomials ◽  
Recurrence Sequences ◽  
Straightforward Extension

We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find convolution formulas for second order linear recurrence polynomials generated by 1 1 + a t + b t 2 x . The case of generating functions containing parameters, even in the numerator is considered. Convolution formulas and general recurrence relations are derived. Many illustrative examples and a straightforward extension to the case of matrix polynomials are shown.

scholarly journals On linear recurrence sequences with polynomial coefficients

1996 ◽  
Vol 38 (2) ◽  
pp. 147-155 ◽  
Author(s):  
A. J. van der Poorten ◽  
I. E. Shparlinski
Keyword(s):  
Recurrence Relation ◽  
Upper Bound ◽  
Rational Numbers ◽  
Negative Integer ◽  
Linear Recurrence ◽  
Initial Values ◽  
Polynomial Coefficients ◽  
Image Position ◽  
Recurrence Sequences

We consider sequences (Ah)defined over the field ℚ of rational numbers and satisfying a linear homogeneous recurrence relationwith polynomial coefficients sj;. We shall assume without loss of generality, as we may, that the sj, are defined over ℤ and the initial values A0A]…, An−1 are integer numbers. Also, without loss of generality we may assume that S0 and Sn have no non-negative integer zero. Indeed, any other case can be reduced to this one by making a shift h → h – l – 1 where l is an upper bound for zeros of the corresponding polynomials (and which can be effectively estimated in terms of their heights)

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