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

• Autorzy: Wladimir de Azevedo Pribitkin
• Języki publikacji: EN

Kategorie tematyczne

• 11F30: Fourier coefficients of automorphic forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 93
• Numer: 4
• Strony: 343-358

Daty

wydano

2000

otrzymano

1999-07-05

poprawiono

1999-10-25

Twórcy

autor

Wladimir de Azevedo Pribitkin

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

Bibliografia

• [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.