@article{bwmeta1.element.bwnjournal-article-aav91i4p291bwm, author = {Wladimir de Azevedo Pribitkin}, title = {The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, I}, journal = {Acta Arithmetica}, volume = {89}, year = {1999}, pages = {291-309}, zbl = {0944.11014}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav91i4p291bwm} }
Wladimir de Azevedo Pribitkin. The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, I. Acta Arithmetica, Tome 89 (1999) pp. 291-309. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav91i4p291bwm/
[000] [1] D. Goldfeld and P. Sarnak, Sums of Kloosterman sums, Invent. Math. 71 (1983), 243-250. | Zbl 0507.10029
[001] [2] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 5th ed., Academic Press, New York, 1994. | Zbl 0918.65002
[002] [3] M. Knopp, Fourier series of automorphic forms of nonnegative dimension, Illinois J. Math. 5 (1961), 18-42. | Zbl 0146.11201
[003] [4] M. Knopp, Automorphic forms of nonnegative dimension and exponential sums, Michigan Math. J. 7 (1960), 257-287. | Zbl 0154.08701
[004] [5] M. Knopp, On the Fourier coefficients of small positive powers of θ(τ), Invent. Math. 85 (1986), 165-183.
[005] [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.
[006] [7] M. Knopp, Modular Functions in Analytic Number Theory, Chelsea, New York, 1993.
[007] [8] J. Lehner, Discontinuous Groups and Automorphic Functions, Amer. Math. Soc., Providence, RI, 1964. | Zbl 0178.42902
[008] [9] D. Niebur, Automorphic integrals of arbitrary positive dimension and Poincaré series, Doctoral Dissertation, University of Wisconsin, Madison, 1968.
[009] [10] D. Niebur, Construction of automorphic forms and integrals, Trans. Amer. Math. Soc. 191 (1974), 373-385. | Zbl 0306.30023
[010] [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. | Zbl 56.0330.02
[011] [12] H. Petersson, Über die Entwicklungskoeffizienten der automorphen Formen, Acta Math. 58 (1932), 169-215. | Zbl 58.1110.01
[012] [13] H. Petersson, Automorphe Formen als metrische Invarianten, Math. Nachr. 1 (1948), 158-212. | Zbl 0031.12503
[013] [14] W. Pribitkin, The Fourier coefficients of modular forms and modular integrals having small positive weight, Doctoral Dissertation, Temple University, Philadelphia, 1995. | Zbl 1161.11336
[014] [15] H. Rademacher, The Fourier coefficients of the modular invariant J(τ), Amer. J. Math. 60 (1938), 501-512. | Zbl 64.0122.01
[015] [16] H. Rademacher, The Fourier series and the functional equation of the absolute modular invariant J(τ), ibid. 61 (1939), 237-248. | Zbl 65.0351.02
[016] [17] H. Rademacher, Correction, ibid. 64 (1942), 456.
[017] [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. | Zbl 0019.02201
[018] [19] W. Roelcke, Das Eigentwertproblem der automorphen Formen in der hyperbolischen Ebene I, Math. Ann. 167 (1966), 292-337. | Zbl 0152.07705
[019] [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.