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Title

Arithmetic of half integral weight theta-series

Authors 1

Affiliations

  1. Department of Mathematics, Seoul National University, Seoul 151-742, Korea

Bibliography

  1. [A1] A. N. Andrianov, Quadratic Forms and Hecke Operators, Grundlehren Math. Wiss. 286, Springer, 1987.
  2. [A2] A. N. Andrianov, The multiplicative arithmetic of Siegel modular forms, Russian Math. Surveys 34 (1979), 75-148.
  3. [A-M] A. N. Andrianov and G. N. Maloletkin, The behavior of theta-series of genus n under modular substitution, Math. USSR-Izv. 9 (1975), 227-241.
  4. [C] H. Cartan, Fonctions Automorphes, Séminaire H. Cartan, 10e année, Vol. I, II, Secrétariat Math., 1958.
  5. [C-J] R. Carlsson und W. Johannssen, Der Multiplikator von Thetareihen höheren Grades zu quadratischen Formen ungerader Ordnung, Math. Z. 177 (1981), 439-447.
  6. [F] E. Freitag, Siegelsche Modulfunktionen, Springer, 1983.
  7. [KKO] M.-H. Kim, J. K. Koo and Y. Y. Oh, Commuting relation between the Siegel operator and Hecke operators on half integral weight Siegel modular forms, preprint.
  8. [Koe] M. Koecher, Zur Theorie der Modulformen n-ten Grades. I, II, Math. Z. 59 (1954), 399-416; Math. Z. 61 (1955), 455-466.
  9. [M] H. Maass, Siegel's Modular Forms and Dirichlet Series, Lecture Notes in Math. 216, Springer, 1971.
  10. [Og] A. Ogg, Modular Forms and Dirichlet Series, Benjamin, 1969.
  11. [O] O. T. O'Meara, Introduction to Quadratic Forms, Grundlehren Math. Wiss. 117, Springer, 1963.
  12. [Sc] R. Schulze-Pillot, Thetareihen positiv definiten quadratische Formen, Invent. Math. 75 (1984), 283-299.
  13. [S1] G. Shimura, On certain reciprocity laws for theta functions and modular forms, Acta Math. 141 (1978), 35-71.
  14. [S2] G. Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440-481.
  15. [S3] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton Univ. Press, 1971.
  16. [Si1] C. L. Siegel, Über die analytische Theorie der quadratischen Formen, I, II, III, Ann. of Math. 36 (1935), 527-606; Ann. of Math. 37 (1936), 230-263; Ann. of Math. 38 (1937), 212-291.
  17. [Si2] C. L. Siegel, Lectures on Analytic Theory of Quadratic Forms, revised ed., IAS and Princeton Univ. Press, 1949.
  18. [St] R. Styer, Prime determinant matrices and the symplectic theta functions, Amer. J. Math. 106 (1984), 645-664.
  19. [Z] N. A. Zharkovskaya, The Siegel operator and Hecke operators, Functional Anal. Appl. 8 (1974), 113-120.
  20. [Zh1] V. G. Zhuravlev, Hecke rings for a covering of the symplectic groups, Math. USSR-Sb. 49 (1984), 379-399.
  21. [Zh2] V. G. Zhuravlev, Expansions of theta-transformations of Siegel modular forms of half integral weight and their analytic properties, Math. USSR-Sb. 51 (1985), 169-190.
Acta Arithmetica
1993/63/2
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Pages:
157-181
Main language of publication
English
Received
1992-03-31
Published
1993
Exact and natural sciences