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

Wladimir de Azevedo Pribitkin

Acta Arithmetica (1999)

  • Volume: 91, Issue: 4, page 291-309
  • ISSN: 0065-1036

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Wladimir de Azevedo Pribitkin. "The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, I." Acta Arithmetica 91.4 (1999): 291-309. <http://eudml.org/doc/207357>.

@article{WladimirdeAzevedoPribitkin1999,
author = {Wladimir de Azevedo Pribitkin},
journal = {Acta Arithmetica},
keywords = {Fourier coefficients; modular forms; Niebur modular integrals; cusp forms; Selberg's Kloosterman zeta-function},
language = {eng},
number = {4},
pages = {291-309},
title = {The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, I},
url = {http://eudml.org/doc/207357},
volume = {91},
year = {1999},
}

TY - JOUR
AU - Wladimir de Azevedo Pribitkin
TI - The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, I
JO - Acta Arithmetica
PY - 1999
VL - 91
IS - 4
SP - 291
EP - 309
LA - eng
KW - Fourier coefficients; modular forms; Niebur modular integrals; cusp forms; Selberg's Kloosterman zeta-function
UR - http://eudml.org/doc/207357
ER -

References

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  1. [1] D. Goldfeld and P. Sarnak, Sums of Kloosterman sums, Invent. Math. 71 (1983), 243-250. Zbl0507.10029
  2. [2] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 5th ed., Academic Press, New York, 1994. Zbl0918.65002
  3. [3] M. Knopp, Fourier series of automorphic forms of nonnegative dimension, Illinois J. Math. 5 (1961), 18-42. Zbl0146.11201
  4. [4] M. Knopp, Automorphic forms of nonnegative dimension and exponential sums, Michigan Math. J. 7 (1960), 257-287. Zbl0154.08701
  5. [5] M. Knopp, On the Fourier coefficients of small positive powers of θ(τ), Invent. Math. 85 (1986), 165-183. 
  6. [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. [7] M. Knopp, Modular Functions in Analytic Number Theory, Chelsea, New York, 1993. 
  8. [8] J. Lehner, Discontinuous Groups and Automorphic Functions, Amer. Math. Soc., Providence, RI, 1964. Zbl0178.42902
  9. [9] D. Niebur, Automorphic integrals of arbitrary positive dimension and Poincaré series, Doctoral Dissertation, University of Wisconsin, Madison, 1968. 
  10. [10] D. Niebur, Construction of automorphic forms and integrals, Trans. Amer. Math. Soc. 191 (1974), 373-385. Zbl0306.30023
  11. [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. Zbl56.0330.02
  12. [12] H. Petersson, Über die Entwicklungskoeffizienten der automorphen Formen, Acta Math. 58 (1932), 169-215. Zbl58.1110.01
  13. [13] H. Petersson, Automorphe Formen als metrische Invarianten, Math. Nachr. 1 (1948), 158-212. Zbl0031.12503
  14. [14] W. Pribitkin, The Fourier coefficients of modular forms and modular integrals having small positive weight, Doctoral Dissertation, Temple University, Philadelphia, 1995. Zbl1161.11336
  15. [15] H. Rademacher, The Fourier coefficients of the modular invariant J(τ), Amer. J. Math. 60 (1938), 501-512. Zbl64.0122.01
  16. [16] H. Rademacher, The Fourier series and the functional equation of the absolute modular invariant J(τ), ibid. 61 (1939), 237-248. Zbl65.0351.02
  17. [17] H. Rademacher, Correction, ibid. 64 (1942), 456. 
  18. [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. Zbl0019.02201
  19. [19] W. Roelcke, Das Eigentwertproblem der automorphen Formen in der hyperbolischen Ebene I, Math. Ann. 167 (1966), 292-337. Zbl0152.07705
  20. [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. 

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