scholarly journals Modular hyperbolas and Beatty sequences

2020 ◽  
Vol 208 ◽  
pp. 148-167
Author(s):  
Marc Technau
Keyword(s):  
Beatty Sequences

scholarly journals Beatty sequences and Langford sequences

1993 ◽  
Vol 111 (1-3) ◽  
pp. 165-178 ◽  
Author(s):  
Roger B. Eggleton ◽  
Aviezri S. Fraenkel ◽  
R.Jaime Simpson
Keyword(s):  
Beatty Sequences

scholarly journals Characterization of two-distance sequences

1992 ◽  
Vol 53 (2) ◽  
pp. 198-218 ◽  
Author(s):  
W. F. Lunnon ◽  
P. A. B. Pleasants
Keyword(s):  
Formal Languages ◽  
Minimal Word ◽  
Beatty Sequences ◽  
Straight Lines ◽  
Symbol Sequences ◽  
Number Of Authors

AbstractThree differently defined classes of two-symbol sequences, which we call the two-distance sequences, the linear sequences and the characteristic sequences, have been discussed by a number of authors and some equivalences between them are known. We present a self-contained proof that the three classes are the same (when ambiguous cases of linear sequences are suitably in terpreted). Associated with each sequence is a real invariant (having a different appropriate definition for each of the three classes). We give results on the relation between sequences with the same invariant and on the symmetry of the sequences. The sequences are closely related to Beatty sequences and occur as digitized straight lines and quasicrystals. They also provide examples of minimal word proliferation in formal languages.

scholarly journals Extended Bounds of Beatty Sequence Associated with Primes

2019 ◽  
Vol 8 (6S3) ◽  
pp. 115-118
Keyword(s):  
Character Sums ◽  
Beatty Sequences ◽  
Composite Moduli ◽  
Beatty Sequence

This paper discusses on the estimation of character sums with respect to non-homogeneous Beatty sequences, over prime where , and is irrational. In particular, the bounds is found by extending several properties of character sums associated with composite moduli over prime. As a result, the bound of is deduced.

scholarly journals Waring’s problem for Beatty sequences and a local to global principle

2014 ◽  
Vol 26 (1) ◽  
pp. 1-16 ◽  
Author(s):  
William D. Banks ◽  
Ahmet M. Güloğlu ◽  
Robert C. Vaughan
Keyword(s):  
Waring’S Problem ◽  
Waring's Problem ◽  
Beatty Sequences ◽  
Global Principle

A Study on Beatty Sequences

2018 ◽  
Vol 10 (2) ◽  
pp. 110-120
Author(s):  
Min-Ji Song ◽  
◽  
Deok Hoon Boo ◽  
Keyword(s):  
Beatty Sequences

Cancellation of Cusp Forms Coefficients over Beatty Sequences on GL(m)

2011 ◽  
Vol 54 (4) ◽  
pp. 757-762
Author(s):  
Qingfeng Sun
Keyword(s):  
Cusp Form ◽  
Fourier Coefficients ◽  
Cusp Forms ◽  
Maass Cusp Form ◽  
Beatty Sequences

AbstractLet A(n1, n2, … , nm–1) be the normalized Fourier coefficients of a Maass cusp form on GL(m). In this paper, we study the cancellation of A(n1, n2, … , nm–1) over Beatty sequences.

Beatty sequences and the arithmetical hierarchy

2017 ◽  
pp. 126-133
Author(s):  
Mehdi Ghasemi ◽  
Mojtaba Moniri
Keyword(s):  
Arithmetical Hierarchy ◽  
Beatty Sequences

scholarly journals A two-parameter family of an extension of Beatty sequences

2008 ◽  
Vol 308 (20) ◽  
pp. 4578-4588 ◽  
Author(s):  
Shiri Artstein-Avidan ◽  
Aviezri S. Fraenkel ◽  
Vera T. Sós
Keyword(s):  
Parameter Family ◽  
Beatty Sequences ◽  
Two Parameter
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