Shimura correspondence of Maass wave forms of half integral weight

• Autorzy: Hisashi Kojima
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 69
• Numer: 4
• Strony: 367-385

Daty

wydano

1995

otrzymano

1992-12-29

poprawiono

1994-02-01

Twórcy

autor

Hisashi Kojima

• Department of Mathematics, the University of Electro-Communications, Chofu-shi, Tokyo 182, Japan

Bibliografia

• [1] T. Asai, On the Doi-Naganuma lifting associated with imaginary quadratic fields, Nagoya Math. J. 71 (1978), 149-167.
• [2] K. Doi and T. Miyake, Automorphic Forms and Number Theory, Kinokuniya Book Store, 1974 (in Japanese).
• [3] S. Friedberg, On the imaginary quadratic Doi-Naganuma lifting of modular forms of arbitrary level, Nagoya Math. J. 92 (1983), 1-20.
• [4] S. Friedberg, On Maass wave forms and the imaginary quadratic Doi-Naganuma lifting, Math. Ann. 263 (1983), 483-508.
• [5] S. Gelbert and I. Piatetski-Shapiro, On Shimura's correspondence for modular forms of half-integral weight, in: Proc. Internat. Colloq. Automorphic Forms, Representation Theory and Arithmetic, 1979, Tata Institute, Springer, 1981, 1-39.
• [6] D. A. Hejhal, Some Dirichlet series with coefficients related to periods of automorphic eigenforms, Proc. Japan Acad. 58 (1982), 413-417.
• [7] S. Niwa, Modular forms of half integral weight and the integral of certain theta-functions, Nagoya Math. J. 56 (1974), 147-161.
• [8] T. Oda, On modular forms associated with indefinite quadratic forms of signature (2,n-2), Math. Ann. 231 (1978), 97-144.
• [9] S. Rallis and G. Schiffmann, On a relation between S͠L cusp forms and cusp forms on tube domains associated to orthogonal groups, Trans. Amer. Math. Soc. 263 (1981), 1-58.
• [10] P. Sarnak, Additive number theory and Maass forms, Lecture Notes in Math. 1052, Springer, Berlin, 1984, 286-309.
• [11] G. Shimura, On modular forms of half integral weight, Ann. of Math. 97 (1973), 440-481.
• [12] T. Shintani, On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J. 58 (1975), 83-126.
• [13] J.-L. Waldspurger, Correspondence de Shimura, J. Math. Pures Appl. 59 (1980), 1-133.