Table of Contents
Journal of Numbers
Volume 2014, Article ID 314173, 7 pages
http://dx.doi.org/10.1155/2014/314173
Research Article

On a Rankin-Selberg -Function over Different Fields

Department of Mathematics, St. Ambrose University, 518 W. Locust Street, Davenport, IA 52803, USA

Received 5 February 2014; Accepted 7 April 2014; Published 27 April 2014

Academic Editor: Emrah Kılıç

Copyright © 2014 Tim Gillespie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Rankin, “Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions, I and II,” Proceedings of the Cambridge Philosophical Society, vol. 35, pp. 351–372, 1939. View at Google Scholar
  2. A. Selberg, “Bermerkungen uber eine Dirichletsche Reihe, die mit der Modulformen nahe verbunden ist,” Archiv for Mathematik og Naturvidenskab, vol. 43, pp. 47–50, 1940. View at Google Scholar
  3. A. Selberg, “On the estimation of Fourier coefficients of modular forms,” in Proceedings of Symposia in Pure Mathematics, vol. 8, pp. 1–15, American Mathematical Society, 1965. View at Google Scholar
  4. H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika, “Rankin-Selberg convolutions,” The American Journal of Mathematics, vol. 105, pp. 367–464, 1983. View at Google Scholar
  5. H. Jacquet and J. A. Shalika, “On Euler products and the classification of automorphic representations I, II,” The American Journal of Mathematics, vol. 103, pp. 499–558, 777–815, 1981. View at Google Scholar
  6. J. Liu and Y. Ye, “Selberg's orthogonality conjecture for automorphic L-functions,” The American Journal of Mathematics, vol. 127, no. 4, pp. 837–849, 2005. View at Google Scholar · View at Scopus
  7. J. Liu and Y. Ye, “Zeros of automorphic L-functions and noncyclic base change,” in Number Theory: Tradition and Modernization, pp. 119–152, Springer, New York, NY, USA, 2005. View at Google Scholar
  8. J. Liu and Y. Ye, “Correlation of zeros of automorphic L-functions,” Science in China, Series A: Mathematics, vol. 51, no. 7, pp. 1147–1166, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Liu and Y. Ye, “Functoriality of automorphic L-functions through their zeros,” Science in China, Series A: Mathematics, vol. 52, no. 1, pp. 1–16, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. F. Shahidi, “On certain L-functions,” The American Journal of Mathematics, vol. 103, pp. 297–355, 1981. View at Google Scholar
  11. C. Moeglin and J. L. Waldspurger, “Le spectre résiduel de GLn,” Annales Scientifiques de l'École Normale Supérieure, vol. 22, no. 4, pp. 605–674, 1989. View at Google Scholar
  12. H. Jacquet, “Principal L-functions of the linear group,” Proceedings of Symposia in Pure Mathematics, vol. 33, part 2, pp. 63–86, 1979. View at Google Scholar
  13. J. Arthur L, Clozel, Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula, vol. 120 of Annals of Mathematics Studies, Princeton University Press, 1989.
  14. Z. Rudnick and P. Sarnak, “Zeros of principal L-functions and random matrix theory,” Duke Mathematical Journal, vol. 88, pp. 269–322, 1996. View at Google Scholar
  15. T. Gillespie and G. Ji, “Prime number theorems for Rankin-Selberg L-functions over number fields,” Science China Mathematics, vol. 54, no. 1, pp. 35–46, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. T. Gillespie, “Factorization of automorphic L-functions and their zero statistics,” International Journal of Number Theory, vol. 9, no. 6, p. 1367, 2013. View at Google Scholar
  17. J. W. Cogdell and I. I. Piatetski-Shapiro, “Converse theorems for GLn,” Publications Mathématiques de L'Institut des Hautes Scientifiques, vol. 79, no. 1, pp. 157–214, 1994. View at Publisher · View at Google Scholar · View at Scopus
  18. H. H. Kim, “An example of non-normal quintic automorphic induction and modularity of symmetric powers of cusp forms of icosahedral type,” Inventiones Mathematicae, vol. 156, no. 3, pp. 495–502, 2004. View at Publisher · View at Google Scholar · View at Scopus
  19. J. Rogawski, “Functoriality and the artin conjecture,” Proceedings of Symposia in Pure Mathematics, vol. 61, pp. 331–353, 1997. View at Google Scholar
  20. D. Ramakrishnan, “Modularity of the Rankin-Selberg L-series, and multiplicity one for SL(2),” Annals of Mathematics, vol. 152, no. 1, pp. 45–111, 2000. View at Google Scholar · View at Scopus