Research and Innovation Articles
Published 2023-03-01
Keywords
- Burnside ring,
- Zeta function,
- Fiber product
How to Cite
Ramírez-Contreras, J. M., Villa-Hernández, D., & Vázquez-Rosas, C. (2023). Zeta function of the Burnside ring for Cp3. Revista Integración, Temas De matemáticas, 41(1), 1–26. https://doi.org/10.18273/revint.v41n1-2023001
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This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
The main objective of this paper is to determine the local and global Zeta function of B(C_{p^3}) the Burnside ring for cyclic groups of order p^3 and to study some relations that fulfill this Zeta function.
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References
- Carlsson, G., "Equivariant stable homotopy and Segal’s Burnside ring conjecture", Ann. Math. 120 (2) (1984) 189-224.
- Carlsson, G., Segal’s Burnside ring conjecture and related problems in topology, in: Proceedings of the International Congress of Mathematicians, Amer. Math. Soc., Berkeley, Calif., Vol. 1, 2, 1986, pp. 574-579.
- Bouc S., Burnside rings, in: Handbook of algebra, North-Holland, Amsterdam, vol 2, 2000, pp. 739-804.
- Bushnell C. J. and Reiner I., "Zeta functions of arithmetic orders and Solomon’s conjectures", Math. Z. 173 (1980) 135-161.
- Bushnell C. J. and Reiner I., "New asymptotic formulas for the distribution of left ideals of orders", Math. 364 (1986) 149-170.
- Ramírez-Contreras J. M. and Villa-Hernández D., "Solomon’s Zeta function of Bp Cp3", Int. Electron. J. Algebra 20 (2016) 1-27.
- Reiner I., Maximal Orders, Academic Press, London New York, 1975.
- Reiner I., "Zeta functions of integral representations", Comm. in Algebra 8 (1980) 911-925.
- Solomon L., "Zeta Functions and Integral Representation Theory", Advances in Math. 26 (1977) 306-326.
- Villa-Hernández D., "Zeta functions of Burnside rings of grups of order p and p2 ", Communications in Algebra, 37 (2009) 1758-1786.
- Villa-Hernández D., "Zeta function of the Burnside ring for cyclic groups", Int. J. Algebra 5 (26) (2011) 1255-1266.
- Villa-Hernández D., "Functional Equations for Zeta functions of Burnside rings", JP J. Algebra Number Theory Appl. 29 (1) (2013) 1-16.
- Wolfram Research, Inc., Mathematica, Version 10.0, Champaign, IL, 2014.