Skip to main content
SpringerLink
Log in
Book cover

Modular Functions of one Variable V pp 247–275Cite as

Units in the modular function field

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 601))

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.99
Price excludes VAT (USA)
  • 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.

Bibliography

  1. B. BIRCH and H. SWINNERTON-DYER, Notes on elliptic curves II, J. reine angew. Math. 218 (1965) pp. 79–108.

    MathSciNet  MATH  Google Scholar 

  2. V. A. DEMJANENKO, On the uniform boundedness of the torsion of elliptic curves over algebraic number fields, Math. USSR Izvestija Vol. 6 (1972) No. 3 pp. 477–490

    Article  Google Scholar 

  3. V. G. DRINFELD, Two theorems on modular curves, Functional analysis and its applications, Vol. 7 No. 2, AMS translation from the Russian, April–June 1973, pp. 155–156

    Google Scholar 

  4. R. FRICKE, Über die Substitutionsgruppen, welche zu den aus dem Legendre'schen Integralmodul k2(θ) gezogenen Wurzeln gehören, Math. Ann. 28 (1887) pp. 99–118

    Article  Google Scholar 

  5. D. KUBERT, Quadratic relations for generators of units in the modular function field, Math. Ann. 225 (1977) pp. 1–20

    Article  MathSciNet  MATH  Google Scholar 

  6. _____, A system of free generators for the universal even ordinary Z(2) distribution on Q2k/z2k, Math. Ann. 224 (1976) pp. 21–31

    Article  MathSciNet  MATH  Google Scholar 

  7. _____, Universal bounds on the torsion of elliptic curves, J. London Math. Soc. to appear

    Google Scholar 

  8. D. KUBERT and S. LANG, Units in the modular function field, Math. Ann.: I, 1975, pp. 67–96

    Article  MathSciNet  Google Scholar 

  9. : II, 1975, pp. 175–189

    Article  MathSciNet  Google Scholar 

  10. : III, 1975, pp. 273–285

    Article  MathSciNet  Google Scholar 

  11. : IV, 1977, pp. 223–242

    Article  MathSciNet  Google Scholar 

  12. ______, Distributions on toroidal groups, Math. Z. 148 (1976) pp. 33–51

    Article  MathSciNet  MATH  Google Scholar 

  13. S. LANG, Elliptic Functions, Addison Wesley, 1973

    Google Scholar 

  14. _____, Division points on curves, Ann. Mat. pura et appl. IV, Tomo LXX (1965) pp. 229–234

    Article  Google Scholar 

  15. _____, Integral points on curves, Pub. IHES No. 6 (1960) pp. 27–43

    Google Scholar 

  16. J. MANIN, Parabolic points and zeta functions of modular curves, Izv. Akad. Nauk SSSR, Ser. Mat. Tom 36 (1972) No. 1, AMS translation pp. 19–64

    Article  MathSciNet  MATH  Google Scholar 

  17. A. NÉRON, Quasi-fonctions et hauteurs sur les variétés abéliennes, Ann. Math. 82 (1965) pp. 249–331

    Article  MATH  Google Scholar 

  18. M. NEWMAN, Construction and application of a class of modular functions, Proc. London Math. Soc. (3) (1957) pp. 334–350

    Google Scholar 

  19. A. OGG, Rational points on certain elliptic modular curves, AMS conference St. Louis, 1972, pp. 221–231

    Google Scholar 

  20. K. RAMACHANDRA, Some applications of Kronecker's limit formula, Ann. Math. 80 (1964) pp. 104–148

    Article  MathSciNet  MATH  Google Scholar 

  21. G. ROBERT, Unités elliptiques, Bull. Soc. Math. France, Mémoire No. 36 (1973)

    Google Scholar 

  22. _____, Nombres de Hurwitz et unités elliptiques, to appear

    Google Scholar 

  23. D. ROHRLICH, Modular functions and the Fermat curve, to appear

    Google Scholar 

  24. C. L. SIEGEL, Lectures on advanced analytic number theory, Tate Institute Notes, 1961, 1965

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Cornell University, 14850, Ithaca, N.Y.

    Dan Kubert

  2. Department of Mathematics, Yale University, 06520, New Haven, Conn.

    Serge Lang

Authors
  1. Dan Kubert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Serge Lang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jean-Pierre Serre Don Bernard Zagier

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Springer-Verlag

About this paper

Cite this paper

Kubert, D., Lang, S. (1977). Units in the modular function field. In: Serre, JP., Zagier, D.B. (eds) Modular Functions of one Variable V. Lecture Notes in Mathematics, vol 601. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063950

Download citation

  • DOI: https://doi.org/10.1007/BFb0063950

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08348-1

  • Online ISBN: 978-3-540-37291-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation