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All issues Volume 244 (2020) EPJ Web Conf., 244 (2020) 01008 References
Open Access
Issue
EPJ Web Conf.
Volume 244, 2020
Complexity and Disorder Meetings 2018-2019-2020
Article Number 01008
Number of page(s) 5
DOI https://doi.org/10.1051/epjconf/202024401008
Published online 15 October 2020
  1. J.-P. Allouche, The zeta-regularized product of odious numbers, Adv. in Appl. Math. (2019) to appear. https://doi.org/10.1016/j.aam.2019.101944. [Google Scholar]
  2. J.-P. Allouche, H. Cohen, Dirichlet series and curious infinite products, Bull. London Math. Soc. 17, 531–538 (1985). [CrossRef] [Google Scholar]
  3. J.-P. Allouche, M. Mendès France, J. Peyrière, Automatic Dirichlet series, J. Number Theory 81, 359–373 (2000). [Google Scholar]
  4. J. Borwein, D. Bailey, R. Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery (Taylor & Francis, 2004). [CrossRef] [Google Scholar]
  5. I. V. Blagouchine, Three notes on Ser’s and Hasse’s representations for the zeta-function, Integers 18A, Paper §A3 (2018). [Google Scholar]
  6. C. Deninger, On the Γ-factors attached to motives, Invent. Math. 104, 245–261 (1991). [Google Scholar]
  7. U. K. Dutta, S. Sangeeta Pradhan, P. K. Ray, Regularized products over balancing and Lucas-balancing numbers, Indian J. Math. 60, 171–179 (2018). [Google Scholar]
  8. S. Egami, Some curious Dirichlet series, in Analytic number theory and its interactions with other parts of number theory (Kyoto, 1998), Su¯rikaisekikenkyu¯sho Ko¯kyu¯roku 1091 (1999), 172–174. [Google Scholar]
  9. H. W. Gould, Temba Shonhiwa, A catalog of interesting Dirichlet series, Missouri J. Math. Sci. 20, 2–18 (2008). [CrossRef] [Google Scholar]
  10. S. W. Hawking, Zeta function regularization of path integrals in curved spacetime, Comm. Math. Phys. 55, 133–148 (1977). [CrossRef] [MathSciNet] [Google Scholar]
  11. K. Kimoto, M. Wakayama, Remarks on zeta regularized products, Int. Math. Res. Not. 2004, 855–875 (2004). [CrossRef] [Google Scholar]
  12. K. Kimoto, N. Kurokawa, C. Sonoki, M. Wakayama, Some examples of generalized zeta regularized products, Kodai Math. J. 27, 321–335 (2004). [CrossRef] [Google Scholar]
  13. A. R. Kitson, The regularized product of the Fibonacci numbers, Preprint (2006), electronically available at https://arXiv.org/abs/math/0608187. [Google Scholar]
  14. N. Kurokawa, M. Wakayama, A generalization of Lerch’s formula, Czechoslovak Math. J. 54, 941–947 (2004). [CrossRef] [Google Scholar]
  15. N. Kurokawa, M. Wakayama, Generalized zeta regularizations, quantum class number formulas, and Appell’s O-functions, Ramanujan J. 10, 291–303 (2005). [CrossRef] [Google Scholar]
  16. E. Landau, A. Walfisz, Über die Nichtfortsetzbarkeit einiger durch Dirichletsche Reihen definierter Funktionen, Rend. Circ. Mat. Palermo 44, 82–86 (1920). [CrossRef] [Google Scholar]
  17. Y. Mizuno, Generalized Lerch formulas: examples of zeta-regularized products, J. Number Theory 118, 155–171 (2006). [CrossRef] [Google Scholar]
  18. E. Muñoz García, R. Pérez Marco, The product over all primes is 4π2, Comm. Math. Phys. 277, 69–81 (2008). [Google Scholar]
  19. L. Navas, Analytic continuation of the Fibonacci Dirichlet series, Fibonacci Quart. 39, 09–418 (2001). [Google Scholar]
  20. On-Line Encyclopedia of Integer Sequences, founded by N. J. A. Sloane, electronically available at http://oeis.org. [Google Scholar]
  21. H. Ostmann, Additive Zahlentheorie I, Ergebnisse der Math. u. ihrer Grenzgebiete, Springer, 1956. [Google Scholar]
  22. J. R. Quine, S. H. Heydari, R. Y. Song, Zeta regularized products, Trans. Amer. Math. Soc. 338, 213–231 (1993). [CrossRef] [Google Scholar]
  23. S. S. Rout, G. K. Panda, Balancing Dirichlet series and related L-functions. Indian J. Pure Appl. Math. 45, (2014), 943–952 (2014). [CrossRef] [Google Scholar]
  24. V. V. Smirnov, The ζ-regularized product over all primes, Preprint (2015), electronically available at https://arXiv.org/abs/1503.06954. [Google Scholar]
  25. C. Soulé, D. Abramovich, J.-F. Burnol, J. Kramer, The determinant of Laplace operators, in Lectures on Arakelov Geometry, Cambridge Studies in Advanced Mathematics 33, Cambridge University Press, Cambridge, 1992, pp. 93–114. [Google Scholar]
  26. A. Sourmelidis, On the meromorphic continuation of Beatty Zeta-functions and Sturmian Dirichlet series, J. Number Theory 194, 303–318 (2019). [CrossRef] [Google Scholar]
  27. G. N. Watson, Theorems stated by Ramanujan (VIII): Theorems on divergent series, J. London Math. Soc. 4, 82–86 (1929). [CrossRef] [Google Scholar]

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