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A remark on the Shimura correspondence

  • Winfried Kohnen (a1) (a2)

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In [4] an identity is given which relates the product of two Fourier coefficients of a Hecke eigenform g of half-integral weight and level 4N with N odd and squarefree to the integral of a Hecke eigenform f of even integral weight associated to g under the Shimura correspondence along a geodesic period on the modular curve X0(N) This formula contains as a special case a refinement of a result of Waldspurger [6] about special values of L-series attached to f at the central point.

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References

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1.Atkin, A. O. L. and Lehner, J., Hecke operators on γO(m), Math. Ann. 185 (1970),134160.
2.Flicker, Y., Automorphic forms on covering groups of GL(2), Invert, math. 57 (1980), 119182.
3.Kohnen, W., Newforms of half-integral weight, J. reine angew. Math. 333 (1982), 3272.
4.Kohnen, W., Fourier coefficients of modular forms of half-integral weight, Math. Ann. 271 (1985), 237268.
5.Shimura, G., On modular forms of half-integral weight, Ann. Math. 97 (1973), 440481.
6.Skoruppa, N.-P., Über den Zusammenhang zwischen Jacobiformen und Modulformen halbganzen Gewichts, (Dissertation, Bonn. Math. Schr. 159, 1985).
7.Skoruppa, N.-P. and Zagier, D., A trace formula for Jacobi forms preprint (1986).
8.Waldspurger, J.-L., Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl. 60 (1981), 375484.
9.Waldspurger, J.-L., Correspondances de Shimura et quaternions, (preprint), 1985).
10.Waldspurger, J.-L., Letter to the author of 03 11, 1987.

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