Bounds for frequencies of residues of second-order recurrences modulo p r

Walter Carlip; Lawrence Somer

Mathematica Bohemica (2007)

  • Volume: 132, Issue: 2, page 137-175
  • ISSN: 0862-7959

Abstract

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The authors examine the frequency distribution of second-order recurrence sequences that are not p -regular, for an odd prime p , and apply their results to compute bounds for the frequencies of p -singular elements of p -regular second-order recurrences modulo powers of the prime p . The authors’ results have application to the p -stability of second-order recurrence sequences.

How to cite

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Carlip, Walter, and Somer, Lawrence. "Bounds for frequencies of residues of second-order recurrences modulo $p^r$." Mathematica Bohemica 132.2 (2007): 137-175. <http://eudml.org/doc/250255>.

@article{Carlip2007,
abstract = {The authors examine the frequency distribution of second-order recurrence sequences that are not $p$-regular, for an odd prime $p$, and apply their results to compute bounds for the frequencies of $p$-singular elements of $p$-regular second-order recurrences modulo powers of the prime $p$. The authors’ results have application to the $p$-stability of second-order recurrence sequences.},
author = {Carlip, Walter, Somer, Lawrence},
journal = {Mathematica Bohemica},
keywords = {Lucas; Fibonacci; stability; uniform distribution; recurrence; uniform distribution; recurrence},
language = {eng},
number = {2},
pages = {137-175},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bounds for frequencies of residues of second-order recurrences modulo $p^r$},
url = {http://eudml.org/doc/250255},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Carlip, Walter
AU - Somer, Lawrence
TI - Bounds for frequencies of residues of second-order recurrences modulo $p^r$
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 2
SP - 137
EP - 175
AB - The authors examine the frequency distribution of second-order recurrence sequences that are not $p$-regular, for an odd prime $p$, and apply their results to compute bounds for the frequencies of $p$-singular elements of $p$-regular second-order recurrences modulo powers of the prime $p$. The authors’ results have application to the $p$-stability of second-order recurrence sequences.
LA - eng
KW - Lucas; Fibonacci; stability; uniform distribution; recurrence; uniform distribution; recurrence
UR - http://eudml.org/doc/250255
ER -

References

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  13. 10.1155/S0161171200003240, Int. J. Math. Math. Sci. 23 (2000), 225–241. (2000) MR1757803DOI10.1155/S0161171200003240
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