Duke Mathematical Journal

On shifted convolutions of $\zeta^3(s)$ with automorphic $L$-functions

Nigel J. E. Pitt

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 77, Number 2 (1995), 383-406.

Dates
First available: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077286346

Mathematical Reviews number (MathSciNet)
MR1321063

Zentralblatt MATH identifier
0855.11024

Digital Object Identifier
doi:10.1215/S0012-7094-95-07711-4

Subjects
Primary: 11F30: Fourier coefficients of automorphic forms
Secondary: 11L05: Gauss and Kloosterman sums; generalizations 11M06: $\zeta (s)$ and $L(s, \chi)$

Citation

Pitt, Nigel J. E. On shifted convolutions of ζ 3 ( s ) with automorphic L -functions. Duke Mathematical Journal 77 (1995), no. 2, 383--406. doi:10.1215/S0012-7094-95-07711-4. http://projecteuclid.org/euclid.dmj/1077286346.


Export citation

References

  • [1] A. Adolphson and S. Sperber, Exponential sums and Newton polyhedra, Bull. Amer. Math. Soc. 16 (1987), no. 2, 282–286.
  • [2] A. Adolphson and S. Sperber, Exponential sums and Newton polyhedra, Cohomology and estimates, Ann. of Math. (2) 130 (1989), no. 2, 367–406.
  • [3] A. Adolphson and S. Sperber, Exponential sums on $(\bf G\sb m)\sp n$, Invent. Math. 101 (1990), no. 1, 63–79.
  • [4] E. Bombieri, On exponential sums in finite fields II, Invent. Math. 47 (1978), no. 1, 29–39.
  • [5] P. Deligne, La Conjecture de Weil I, Inst. Hautes Études Sci. Publ. Math. (1974), no. 43, 273–307.
  • [6] J.-M. Deshouillers and H. Iwaniec, Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math. 70 (1982), no. 2, 219–288.
  • [7] W. Duke, J. Friedlander, and H. Iwaniec, Bounds for Automorphic $L$-functions, MSRI, Berkeley, CA, January 1992.
  • [8] W. Duke and H. Iwaniec, Estimates for coefficients of $L$-functions I, preprint.
  • [9] B. Dwork, On the rationality of the zeta-function of an algebraic variety, Amer. J. Math. 82 (1960), 631–648.
  • [10] A. Good, Cusp forms and eigenfunctions of the Laplacian, Math. Ann. 255 (1981), no. 4, 523–548.
  • [11] C. Hooley, On exponential sums and certain of their applications, Number Theory Days, 1980 (Exeter, 1980), London Math. Soc. Lecture Note Ser., vol. 56, Cambridge University Press, Cambridge, 1982, pp. 92–122.
  • [12] H. Iwaniec, Small eigenvalues of Laplacian for $\Gamma\sb 0(N)$, Acta Arith. 56 (1990), no. 1, 65–82.
  • [13] N. Katz, Gauss Sums, Kloosterman Sums and Monodromy Groups, Ann. of Math. Stud., vol. 116, Princeton University Press, Princeton, NJ, 1988.
  • [14] R. Rankin, Modular Forms and Functions, Cambridge University Press, Cambridge, 1977.
  • [15] R. Rankin, Sums of cusp form coefficients, Automorphic Forms and Analytic Number Theory (Montreal, PQ, 1989), Universite de Montreal, Centre de Researches Mathematiques, Montreal, 1990, pp. 115–121.
  • [16] A. Selberg, On the estimation of Fourier coefficients of modular forms, Proc. Sympos. Pure Math., Vol. VIII, Amer. Math. Soc., Providence, R.I., 1965, pp. 1–15.
  • [17] F. Shahidi, On certain $L$-functions, Amer. J. Math. 103 (1981), no. 2, 297–355.
  • [18] F. Shahidi, Third symmetric power $L$-functions for $\rm GL(2)$, Compositio Math. 70 (1989), no. 3, 245–273.
  • [19] F. Shahidi, Automorphic $L$-functions, a survey, Automorphic Forms, Shimura Varieties and $L$-Functions, Vol. I (Ann Arbor, MI, 1988), Perspect. Math., vol. 10, Academic Press, New York, 1990, pp. 415–437.