ArticleOriginal scientific text

Title

The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, II

Authors 1

Affiliations

  1. Department of Mathematics, Princeton University, 607 Fine Hall, Washington Road, Princeton, NJ 08544-1000, U.S.A.

Bibliography

  1. G. Andrews, The Theory of Partitions, Cambridge Univ. Press, Cambridge, 1998.
  2. D. Goldfeld and P. Sarnak, Sums of Kloosterman sums, Invent. Math. 71 (1983), 243-250.
  3. M. Knopp, On the Fourier coefficients of small positive powers of θ(τ), ibid. 85 (1986), 165-183.
  4. M. Knopp, On the Fourier coefficients of cusp forms having small positive weight, in: Proc. Sympos. Pure Math. 49, Part 2, Amer. Math. Soc., Providence, RI, 1989, 111-127.
  5. D. Niebur, Automorphic integrals of arbitrary positive dimension and Poincaré series, Doctoral Dissertation, University of Wisconsin, Madison, 1968.
  6. D. Niebur, Construction of automorphic forms and integrals, Trans. Amer. Math. Soc. 191 (1974), 373-385.
  7. P. Pasles and W. Pribitkin, A generalization of the Lipschitz summation formula and some applications, to appear.
  8. W. Pribitkin, The Fourier coefficients of modular forms and modular integrals having small positive weight, Doctoral Dissertation, Temple University, Philadelphia, 1995.
  9. W. Pribitkin, The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, I, Acta Arith. 91 (1999), 291-309.
  10. H. Rademacher and H. S. Zuckerman, On the Fourier coefficients of certain modular forms of positive dimension, Ann. of Math. 39 (1938), 433-462.
  11. W. Roelcke, Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene I, Math. Ann. 167 (1966), 292-337.
  12. A. Selberg, On the estimation of Fourier coefficients of modular forms, in: Theory of Numbers, Proc. Sympos. Pure Math. 8, Amer. Math. Soc., Providence, RI, 1965, 1-15.
Pages:
343-358
Main language of publication
English
Received
1999-07-05
Accepted
1999-10-25
Published
2000
Exact and natural sciences