Arithmetic of half integral weight theta-series

Myung-Hwan Kim

Acta Arithmetica (1993)

  • Volume: 63, Issue: 2, page 157-181
  • ISSN: 0065-1036

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Myung-Hwan Kim. "Arithmetic of half integral weight theta-series." Acta Arithmetica 63.2 (1993): 157-181. <http://eudml.org/doc/206512>.

@article{Myung1993,
author = {Myung-Hwan Kim},
journal = {Acta Arithmetica},
keywords = {Siegel modular forms of half integral weight; Siegel theta series of quadratic forms; Hecke operators; eigenfunction; eigenvalues},
language = {eng},
number = {2},
pages = {157-181},
title = {Arithmetic of half integral weight theta-series},
url = {http://eudml.org/doc/206512},
volume = {63},
year = {1993},
}

TY - JOUR
AU - Myung-Hwan Kim
TI - Arithmetic of half integral weight theta-series
JO - Acta Arithmetica
PY - 1993
VL - 63
IS - 2
SP - 157
EP - 181
LA - eng
KW - Siegel modular forms of half integral weight; Siegel theta series of quadratic forms; Hecke operators; eigenfunction; eigenvalues
UR - http://eudml.org/doc/206512
ER -

References

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  2. [A2] A. N. Andrianov, The multiplicative arithmetic of Siegel modular forms, Russian Math. Surveys 34 (1979), 75-148. Zbl0427.10017
  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. Zbl0326.10025
  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. Zbl0461.10020
  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. Zbl0055.07704
  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. Zbl0191.38101
  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. Zbl0533.10021
  13. [S1] G. Shimura, On certain reciprocity laws for theta functions and modular forms, Acta Math. 141 (1978), 35-71. Zbl0402.10030
  14. [S2] G. Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440-481. Zbl0266.10022
  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. Zbl0548.10019
  19. [Z] N. A. Zharkovskaya, The Siegel operator and Hecke operators, Functional Anal. Appl. 8 (1974), 113-120. Zbl0314.10021
  20. [Zh1] V. G. Zhuravlev, Hecke rings for a covering of the symplectic groups, Math. USSR-Sb. 49 (1984), 379-399. Zbl0542.10021
  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. Zbl0571.10029

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