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Abstract

Zeta Functions: Symmetry and Applications †

by
Emilio Elizalde
National Higher Research Council of Spain, Institute for Space Sciences, UAB Campus, Carrer de Can Magrans s/n, 08193 Bellaterra (Barcelona), Spain
†
Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017.
Proceedings 2018, 2(1), 38; https://doi.org/10.3390/proceedings2010038
Published: 3 January 2018
(This article belongs to the Proceedings of The First International Conference on Symmetry)
Versions Notes
A short summary of some symmetry properties of the Riemann zeta function and of different zeta functions corresponding to pseudodifferential operators will be given. An introduction to the main issues concerning the zeta-function regularization procedure will follow, with special emphasis on the rigor, power, and universality of the method, contrasting with the sloppy missuses of the same that have appeared too often in the literature. After that, applications of zeta-function regularization in quantum field theory and cosmology will be discussed, together with some important associated problems that can be dealt with by using this method.

References

  1. Elizalde, E. Ten Physical Applications of Spectral Zeta Functions, 2nd ed.; Lecture Notes in Physics; Springer-Verlag: Berlin, Germany, 2012. [Google Scholar]
  2. Elizalde, E. Ten Physical Applications of Spectral Zeta Functions, 1st ed.; Lecture Notes in Physics Monographs; Springer-Verlag: Berlin, Germany, 1995. [Google Scholar]
  3. Elizalde, E.; Odintsov, S.D.; Romeo, A.; Bytsenko, A.A.; Zerbini, S. Zeta Regularization Techniques with Applications; World Scientific: Singapore, 1994. [Google Scholar]
  4. Kirsten, K. Spectral Functions in Mathematics and Physics, 1st ed.; Chapman & Hall: London, UK, 2001. [Google Scholar]
  5. Bytsenko, A.A.; Cognola, G.; Elizalde, E.; Moretti, V.; Zerbini, S. Analytic Aspects of Quantum Fields; World Scientific: Singapore, 2004. [Google Scholar]

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MDPI and ACS Style

Elizalde, E. Zeta Functions: Symmetry and Applications. Proceedings 2018, 2, 38. https://doi.org/10.3390/proceedings2010038

AMA Style

Elizalde E. Zeta Functions: Symmetry and Applications. Proceedings. 2018; 2(1):38. https://doi.org/10.3390/proceedings2010038

Chicago/Turabian Style

Elizalde, Emilio. 2018. "Zeta Functions: Symmetry and Applications" Proceedings 2, no. 1: 38. https://doi.org/10.3390/proceedings2010038

APA Style

Elizalde, E. (2018). Zeta Functions: Symmetry and Applications. Proceedings, 2(1), 38. https://doi.org/10.3390/proceedings2010038

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