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Fourier coefficients of modular forms of half-integral weight

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References

  1. Bateman, H.: Higher transcendental functions II. New York-Toronto-London: McGraw-Hill 1953

    Google Scholar 

  2. Burgess, D.: On character sums and primitive roots. Proc. Lond. Math. Soc. (3)12, 179–192 (1962)

    Google Scholar 

  3. Deligne, P.: La conjécture de Weil I. Publ. Math. Inst. Hautes Etud. Sci.43, 273–307 (1974)

    Google Scholar 

  4. Flicker, Y.: Automorphic forms on covering groups ofGL(2). Invent. math.57, 119–182 (1980)

    Google Scholar 

  5. Gelbart, S.: Weil's representation and the spectrum of the metaplectic group. Lecture Notes in Math., vol. 530. Berlin-Heidelberg-New York: Springer 1976

    Google Scholar 

  6. Goldfeld, D., Hoffstein, J.: Eisenstein series of 1/2-integral weight and the mean value of real DirichletL-series. Invent. math.80, 185–208 (1985)

    Google Scholar 

  7. Hooley, C.: On the greatest prime factor of a cubic polynomial. J. Reine Angew. Math.303/304, 21–50 (1978)

    Google Scholar 

  8. Kohnen, W.: Fourier coefficients of modular forms of half-integral weight. Math. Ann.271, 237–268 (1985)

    Google Scholar 

  9. Mordell, L.J.: The sign of the Gaussian sum. Ill. J. Math.6, 177–180 (1962)

    Google Scholar 

  10. Niwa, S.: Modular forms of half-integral weight and the integral of certain theta-functions. Nagoya Math. J.56, 147–161 (1975)

    Google Scholar 

  11. Petersson, H.: Über die Entwicklungskoeffizienten der automorphen Formen. Acta Math.58, 169–215 (1932)

    Google Scholar 

  12. Rankin, R.: Modular forms and functions. Cambridge-London-New York: Cambridge University Press 1977

    Google Scholar 

  13. Salié, H.: Über die Kloostermanschen SummenS(u, v; q). Math. Z.34, 91–109 (1931)

    Google Scholar 

  14. Serre, J-P., Stark, H.M.: Modular forms of weight 1/2. Springer Lecture Notes in Math., vol. 627, pp. 27–67. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  15. Shintani, T.: On construction of holomorphic cusp forms of half-integral weight. Nagoya Math. J.58, 83–126 (1975)

    Google Scholar 

  16. Shimura, G.: On modular forms of half-integral weight. Ann. Math.97, 440–481 (1973)

    Google Scholar 

  17. Waldspurger, J.-L.: Sur les coefficients de Fourier des formes modulaires de poids demi-entier. J. Math. Pures Appl.60, 375–484 (1981)

    Google Scholar 

  18. Williams, K.S.: Note on Salié's sum. Proc. Am. Math. Soc.30(2), 393–394 (1971)

    Google Scholar 

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  1. School of Mathematics, The Institute for Advanced Study, 08540, Princeton, NJ, USA

    Henryk Iwaniec

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  1. Henryk Iwaniec
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Supported by NSF grant MCS-8108814(A02)

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Iwaniec, H. Fourier coefficients of modular forms of half-integral weight. Invent Math 87, 385–401 (1987). https://doi.org/10.1007/BF01389423

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