Skip to main content

Theta functions over Q and over Q(√q)

Part of the Lecture Notes in Mathematics book series (LNM,volume 627)

Keywords

  • Modular Form
  • Theta Function
  • Clifford Algebra
  • Cusp Form
  • Maximal Lattice

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. COHEN H., Formes modulaires à une et deux variables, Thèse 1976, Université de Bordeaux I

    Google Scholar 

  2. EICHLER M., Quadratische Formen und orthogonale Gruppen, 2. Aufl. Springer Verlag, Berlin-Heidelberg-New York 1974.

    CrossRef  MATH  Google Scholar 

  3. EICHLER M., Zur Zahlentheorie der Quaternionen-Algebren, Journal reine und angew. Math. 195 (1956), 127–151.

    MathSciNet  Google Scholar 

  4. EICHLER M., Quadratische Formen und Modulfunktionen, Acta Arithmetica 4 (1958), 217–239.

    MathSciNet  Google Scholar 

  5. EICHLER M., The basis problem for modular forms and the traces of Hecke operators, in Modular Forms of One Variable I, Lecture Notes in Mathematics nr. 320, Springer Verlag, Berlin-Heidelberg-New York 1973.

    Google Scholar 

  6. EICHLER M., On theta functions in real algebraic number fields, to appear in Acta Arithmetica.

    Google Scholar 

  7. HIJIKATA H. and SAITO H., On the representability of modular forms by theta series, p. 13–21 in Number Theory, Algebraic Geometry, and Commutative Algebra, a volume published in honor of Y. Akizuki, Kinokuniya, Tokyo 1973.

    Google Scholar 

  8. NAGANUMA H., On the coincidence of two Dirichlet series associated with cusp forms of Hecke's “nebentype” and Hilbert modular forms over real quadratic fields, Journ. Math. Soc. Japan (4) 25 (1973), 547–555.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. PETERS M., Ternäre und quaternäre quadratische Formen und Quaternionenalgebren, Acta Arithmetica 15 (1969), 319–365.

    MathSciNet  MATH  Google Scholar 

  10. SAITO H., Automorphic forms and algebraic extensions of number fields, Lecture Note in Mathematics nr. 8, Kyoto Univ. 1975.

    Google Scholar 

  11. SHIMIZU H., On traces of Hecke operators, Journ. Fac. Sci. Univ. Tokyo 10 (1963), 1–19.

    MathSciNet  MATH  Google Scholar 

  12. ZAGIER D., Modular forms associated to real quadratic fields, Inventiones Math. 30 (1975), 1–46.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. O'MEARA O.T., Introduction to Quadratic Forms, Springer Verlag, Berlin-Heidelberg-New York, 1963.

    CrossRef  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1977 Springer-Verlag

About this paper

Cite this paper

Eichler, M. (1977). Theta functions over Q and over Q(√q). In: Serre, JP., Zagier, D.B. (eds) Modular Functions of One Variable VI. Lecture Notes in Mathematics, vol 627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065302

Download citation

  • DOI: https://doi.org/10.1007/BFb0065302

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08530-0

  • Online ISBN: 978-3-540-35984-5

  • eBook Packages: Springer Book Archive