Research and Innovation Articles
Published 2010-06-09
Keywords
- Sidon sets,
- Bh sets
How to Cite
Bravo G., J. J., & Trujillo S., C. A. (2010). Fourier Analysis on Zn and Bh sets. Revista Integración, Temas De matemáticas, 28(1), 67–78. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2060
Abstract
A set A of positive integers is called a Bh set, if all sums ofh elements of A are different. In this paper we use basic properties ofFourier analysis on ZN and follow the style of Ben Green [4] to concludewith a different method, the upper bounds obtained by Jia [6], Chen [2] andGraham [5] with respect to the maximum cardinal that can have a Bh setcontained in the first N positive integers.
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References
[1] Bravo J., “Análisis de Fourier Finito y Conjuntos Bh[g]”, Trabajo de grado, Maestría en Ciencias-Matemáticas, Universidad del Valle, 2006
[2] Chen S., On the Size of Finite Sidon Sequences, Proc. Amer. Math. Soc, 121 (1994), 353–356.
[3] Erdös P. and Turán P., On a Problem of Sidon in Additive Number Theory and On Some Related Problems, Journal of the London Mathematical Society, 16 (1941), 212–215.
[4] Green B., The number of squares and Bh[g] sets, Acta Arithmética, 100 (2001), 365–390.
[5] Graham S. W., Bh Sequences, Analytic Number Theory, 1 (Allerton Park, IL, 1995), 431–449, Progress in Mathematics 138, Birkhäuser, Boston MA, 1996.
[6] Jia X., On B2k Sequences, Journal of Number Theory, 48 (1994), 183–196.
[7] Lindström B., A Remark on B4 Sequences, Journal of Combinatorial Theory, 7 (1969), 276–277.
[8] Singer J., A Theorem in Finite Projective Geometry and Some Applications to Number Theory, Transactions of
the American Mathematical Society, 43 (1938), 377–385.
[9] Terras A., “Fourier Analysis on Finite Groups and Aplications,” Cambridge University Press, second edition, San Francisco, 1999
[2] Chen S., On the Size of Finite Sidon Sequences, Proc. Amer. Math. Soc, 121 (1994), 353–356.
[3] Erdös P. and Turán P., On a Problem of Sidon in Additive Number Theory and On Some Related Problems, Journal of the London Mathematical Society, 16 (1941), 212–215.
[4] Green B., The number of squares and Bh[g] sets, Acta Arithmética, 100 (2001), 365–390.
[5] Graham S. W., Bh Sequences, Analytic Number Theory, 1 (Allerton Park, IL, 1995), 431–449, Progress in Mathematics 138, Birkhäuser, Boston MA, 1996.
[6] Jia X., On B2k Sequences, Journal of Number Theory, 48 (1994), 183–196.
[7] Lindström B., A Remark on B4 Sequences, Journal of Combinatorial Theory, 7 (1969), 276–277.
[8] Singer J., A Theorem in Finite Projective Geometry and Some Applications to Number Theory, Transactions of
the American Mathematical Society, 43 (1938), 377–385.
[9] Terras A., “Fourier Analysis on Finite Groups and Aplications,” Cambridge University Press, second edition, San Francisco, 1999