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Beta Expansion of Pisot Roots with pseudo co-factor
G. Nagendra Kumar1 , E. Keshava Reddy2
Section:Research Paper, Product Type: Journal-Paper
Vol.7 ,
Issue.1 , pp.80-85, Feb-2020
Online published on Feb 28, 2020
Copyright © G. Nagendra Kumar, E. Keshava Reddy . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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IEEE Style Citation: G. Nagendra Kumar, E. Keshava Reddy, “Beta Expansion of Pisot Roots with pseudo co-factor,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.80-85, 2020.
MLA Style Citation: G. Nagendra Kumar, E. Keshava Reddy "Beta Expansion of Pisot Roots with pseudo co-factor." International Journal of Scientific Research in Mathematical and Statistical Sciences 7.1 (2020): 80-85.
APA Style Citation: G. Nagendra Kumar, E. Keshava Reddy, (2020). Beta Expansion of Pisot Roots with pseudo co-factor. International Journal of Scientific Research in Mathematical and Statistical Sciences, 7(1), 80-85.
BibTex Style Citation:
@article{Kumar_2020,
author = {G. Nagendra Kumar, E. Keshava Reddy},
title = {Beta Expansion of Pisot Roots with pseudo co-factor},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {2 2020},
volume = {7},
Issue = {1},
month = {2},
year = {2020},
issn = {2347-2693},
pages = {80-85},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1747},
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1747
TI - Beta Expansion of Pisot Roots with pseudo co-factor
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - G. Nagendra Kumar, E. Keshava Reddy
PY - 2020
DA - 2020/02/28
PB - IJCSE, Indore, INDIA
SP - 80-85
IS - 1
VL - 7
SN - 2347-2693
ER -
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Abstract :
A beta expansion is correspondent to the base 10 representation where base may be real number or non-integer. If is a pisot number, and P(x) is a monic polynomial then where R(x) is the companion polynomial of the expansion P(x) and Q(x) is the polynomial factor which is nonreciprocal converges to 2, it is the limit point of the pisot number. By using greedy expansion with base then the expansion will be either finite or periodic. If and are the limit points of the regular pisot number then the corresponding polynomials can be determined. Some Beta expansions for algebraic integers can be determined if pisot numbers hold the finite reversibly greedy (FRG) beta expansion. This paper gives the expansion for the pisot roots of which satisfies the Finite Reversibly Greedy (FRG) property.
Key-Words / Index Term :
Pisot numbers, Beta expansion, FRG
References :
[1] Victor J Katz, “A history of mathematics”, Harper Collins college publishers, New York 1993 an introduction.
[2] A Renyi, “Representations of real numbers and their ergodic properties”,.Acta math.Acad.Sci.Hungar,8:477-493,1957.
[3] K.G.Hare “Beta-Expansion of pisot and salem numbers.”In computer algebra 2006, pages 67-84 world sci. publ.,Hackensanck,NJ,2007.
[4] C.L.Siegel,”Algrebraic integers whose conjugates lie in the unit circle”,Duke math.J.11(1944)597-602.
[5] M.Amara,”Ensembles fermes de nombres algebriques”, Ann.Sci Ecole Norm.Sup(3) 83(1966) 215-270.
[6] Maysum Panju,”Beta Expansion for regular pisot numbers”,arXiv:1103.2147v, math..NT,10 Mar 2011.
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