Advertisement

Explicit formulas in the theory of automorphic forms

  • C. J. Moreno
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 626)

Keywords

Modular Form Eisenstein Series Cusp Form Dirichlet Series Automorphic Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. N. Andrianov, Euler products corresponding to Siegel modular forms of degree 2, Uspehi Mat. Nauk 29(1974), 43–110.MathSciNetzbMATHGoogle Scholar
  2. [2]
    A. Borel, Formes automorphes et séries de Dirichlet, Sem. Boarbaki, No. 466, June (1975).Google Scholar
  3. [3]
    W. Casselman, On representations of GL 2 and the arithmetic of modular curves, Modular functions of one variable II, Springer L. N. 349 (1973), 107–142.MathSciNetCrossRefGoogle Scholar
  4. [4]
    W. Casselman, On some results of Atkin and Lehner, Math. Ann. 201 (1973), 301–314.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    J. Coates and A. Wiles, On the conjecture of Birch and Swinnerton-Dyer, preprint (1976).Google Scholar
  6. [6]
    H. Davenport, Multiplicative number theory, Markham, Chicago 1967.zbMATHGoogle Scholar
  7. [7]
    P. Deligne, La conjecture de Weil, I, Publ. I. H. E. S. 43(1974), 273–307.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    K. Doi and H. Naganuma, On the functional equation of certain Dirichlet series, Inv. Math. 9(1969), 1–14.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    S. A. Gaal, Linear analysis and representation theory, Springer-Verlag, New York/Berlin 1973.CrossRefzbMATHGoogle Scholar
  10. [10]
    S. Gelbart, Automorphic forms on adele groups, Annals of Math. Studies 83 (1975), Princeton Univ. Press.Google Scholar
  11. [11]
    S. Gelbart and H. Jacquet, A relation between automorphic forms on GL(2) and GL(3), Proc. Natl. Acad. Sci. USA, vol. 73 (1976), 3348–3350.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    I. M. Gelfand, M. I. Graev and I. I. Piateckii-Shapiro, Representation theory and automorphic forms, Saunders, Philadelphia 1969.Google Scholar
  13. [13]
    G. H. Hardy, Ramanujan, Chelsea, New York 1940.zbMATHGoogle Scholar
  14. [14]
    H. Jacquet, Automorphic forms on GL(2), part II, Springer L. N. 278, 1972.Google Scholar
  15. [15]
    H. Jacquet and J. A. Shalika, A non-vanishing theorem for zeta functions of GL n, Inv. Math. 38 (1976), 1–16.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    H. Jacquet and R. P. Langlands, Automorphic forms on GL(2), Springer L. N. 114, 1970.Google Scholar
  17. [17]
    T. Kubota, Elementary theory of Eisenstein series, Kodansha Ltd., Tokyo 1973.zbMATHGoogle Scholar
  18. [18]
    E. Landau, Über die Anzahl der Gitterpunkte in gewissen Bereichen (Part II), Gött. Nachr. (1915), 209–243.Google Scholar
  19. [19]
    S. Lang, Algebraic number theory, Addison-Wesley, Reading, Mass. 1964.Google Scholar
  20. [20]
    S. Lang, Elliptic functions, Addison-Wesley, Reading, Mass. 1973.zbMATHGoogle Scholar
  21. [21]
    S. Lang, On the zeta function of number fields, Inv. Math. 12 (1971), 337–345.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    R. P. Langlands, Base change for GL(2): The theory of Saito-Shintani with applications, preprint, Institute for Advanced Study, Princeton, NJ, 1975.Google Scholar
  23. [23]
    R. P. Langlands, Euler products, Yale Univ. Press, 1967.Google Scholar
  24. [24]
    R. P. Langlands, Problems in the theory of automorphic forms, in Lectures in Modern Analysis and Applications, Springer L. N. 170 (1970), 18–86.MathSciNetGoogle Scholar
  25. [25]
    W. Li, New forms and functional equations, Math. Ann. 212 (1975), 285–315.MathSciNetCrossRefGoogle Scholar
  26. [26]
    H. Maass, Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 121 (1944), 141–182.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and theorems for the special functions of mathematical physics, Springer-Verlag, New York 1966.CrossRefzbMATHGoogle Scholar
  28. [28]
    A. Orihara, On the Eisenstein series for the principal congruence subgroups, Nagoya Math. J. vol. 34(1969), 129–142.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    H. Rademacher, On the Phragmén-Lindelöf Theorem and some applications, Math. Zeitschr. 72(1959), 192–204.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    R. A. Rankin, Contributions to the theory of Ramanujan's function τ(n) and similar arithmetic functions, I, II, Proc. Cambridge Phil. Soc. 35 (1939), 351–372; III, Proc. Cambridge Phil. Soc. 36(1940), 150–151.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    R. A. Rankin, An Ω-result for the coefficients of cusp forms, Math. Ann. 203 (1973), 239–250.MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    I. Satake, Theory of spherical functions on reductive algebraic groups, Publ. I. H. E. S. 18 (1963), 5–69.MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    I. Satake, Spherical functions and Ramanujan conjecture, in Proc. Symp. Pure Math., 9 (1966), 258–264, A. M. S. Providence R.I.MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    L. Schwartz, Theorie des distributions, vol. II, Hermann, Paris 1959.zbMATHGoogle Scholar
  35. [35]
    A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. 20 (1956), 47–81.MathSciNetzbMATHGoogle Scholar
  36. [36]
    F. Shahidi, Functional equation satisfied by certain L-functions, preprint (1976).Google Scholar
  37. [37]
    G. Shimura, Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten and Princeton Univ. Press 1971.Google Scholar
  38. [38]
    G. Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. 31 (1975), 79–98.MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    A. M. Stark, Some effective cases of the Brauer-Siegel Theorem, Inv. Math. 23 (1974), 135–152.MathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    A. Weil, Ueber die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 168 (1967), 149–167.MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    A. Weil, Sur les "formules explicites" de la théorie des nombres premiers, Comm. Sém. Math. Université de Lund (dedié à M. Riesz) (1952), 252–265.Google Scholar
  42. [42]
    A. Weil, Sur les formules explicites de la theorie des nombres, Isv. Acad. Nauk. 36 (1972), 3–18.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • C. J. Moreno

There are no affiliations available

Personalised recommendations