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

• 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: 1999
• Tom: 91
• Numer: 4
• Strony: 291-309

Daty

wydano

1999

otrzymano

1997-08-19

poprawiono

1998-07-21

Twórcy

autor

Wladimir de Azevedo Pribitkin

• Department of Mathematics and Natural Sciences, Centenary College, Hackettstown, NJ 07840, U.S.A.

Bibliografia

• [1] D. Goldfeld and P. Sarnak, Sums of Kloosterman sums, Invent. Math. 71 (1983), 243-250.
• [2] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 5th ed., Academic Press, New York, 1994.
• [3] M. Knopp, Fourier series of automorphic forms of nonnegative dimension, Illinois J. Math. 5 (1961), 18-42.
• [4] M. Knopp, Automorphic forms of nonnegative dimension and exponential sums, Michigan Math. J. 7 (1960), 257-287.
• [5] M. Knopp, On the Fourier coefficients of small positive powers of θ(τ), Invent. Math. 85 (1986), 165-183.
• [6] 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.
• [7] M. Knopp, Modular Functions in Analytic Number Theory, Chelsea, New York, 1993.
• [8] J. Lehner, Discontinuous Groups and Automorphic Functions, Amer. Math. Soc., Providence, RI, 1964.
• [9] D. Niebur, Automorphic integrals of arbitrary positive dimension and Poincaré series, Doctoral Dissertation, University of Wisconsin, Madison, 1968.
• [10] D. Niebur, Construction of automorphic forms and integrals, Trans. Amer. Math. Soc. 191 (1974), 373-385.
• [11] H. Petersson, Theorie der automorphen Formen beliebiger reeller Dimension und ihre Darstellung durch eine neue Art Poincaréscher Reihen, Math. Ann. 103 (1930), 369-436.
• [12] H. Petersson, Über die Entwicklungskoeffizienten der automorphen Formen, Acta Math. 58 (1932), 169-215.
• [13] H. Petersson, Automorphe Formen als metrische Invarianten, Math. Nachr. 1 (1948), 158-212.
• [14] W. Pribitkin, The Fourier coefficients of modular forms and modular integrals having small positive weight, Doctoral Dissertation, Temple University, Philadelphia, 1995.
• [15] H. Rademacher, The Fourier coefficients of the modular invariant J(τ), Amer. J. Math. 60 (1938), 501-512.
• [16] H. Rademacher, The Fourier series and the functional equation of the absolute modular invariant J(τ), ibid. 61 (1939), 237-248.
• [17] H. Rademacher, Correction, ibid. 64 (1942), 456.
• [18] H. Rademacher and H. S. Zuckerman, On the Fourier coefficients of certain modular forms of positive dimension, Ann. of Math. 39 (1938), 433-462.
• [19] W. Roelcke, Das Eigentwertproblem der automorphen Formen in der hyperbolischen Ebene I, Math. Ann. 167 (1966), 292-337.
• [20] 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.