Skip to main content

Gross-Koblitz formula for function fields

  • Chapter
  • First Online:
p-adic Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1454))

  • 1251 Accesses

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

Access this chapter

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 59.95
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Carlitz, On certain functions connected with polynomials in a Galois field, Duke Math.J. (1935),pp.137–168.

    Google Scholar 

  2. L. Carlitz, A class of polynomials, Trans. A.M.S. 43 (1938), pp.167–182.

    Article  MATH  Google Scholar 

  3. V. Drinfeld, Elliptic modules (English translation) Math. Sbornik, vol23,(1974),561–592.

    Article  Google Scholar 

  4. E. U. Gekeler, Drinfeld modular curves, Lecture notes in math. 1231.

    Google Scholar 

  5. D. Goss, von-Staudt for F q[T], Duke Math.J. 45 (1978),pp.885–910.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. Goss, Modular forms for F q[T]. J. reine angew. Math. vol.317, (1980),163–191.

    MathSciNet  Google Scholar 

  7. D. Goss, The Γ-function in the arithmetic of function fields. Duke Math J. vol. 56 (1988), 163–191.

    Article  MathSciNet  MATH  Google Scholar 

  8. B.H. Gross, N. Koblitz, Gauss sums and the p-adic Γ-function. Ann. Math. 109, 569–581 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Hayes, Explicit class field theory for rational function fields. Trans. Am. Math. Soc. 189, 77–91(1974).

    Article  MathSciNet  MATH  Google Scholar 

  10. D. Hayes, Explicit class field theory in global function fields. G.C. Rota (ed), Studies in Algebra and Number theory. Academic press 173–217 (1979)

    Google Scholar 

  11. D. Hayes, Stickelberger elements in function fields. Comp. Math. 55, 209–235 (1985).

    MathSciNet  MATH  Google Scholar 

  12. D. Hayes, The refined ℘-adic abelian Stark conjecture in function fields. Inv. Math. 94, 505–527 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  13. N. Katz, Crystalline cohomology, Dieudonne modules and Jacobi sums. In Automorphic forms, representation theory and arithmetic. (TIFR, Bombay, 1979), 165–245.

    Google Scholar 

  14. D. Thakur, Gamma functions and Gauss sums for function fields and periods of Drinfeld modules. Thesis, Harvard University (1987).

    Google Scholar 

  15. D. Thakur, Gauss sums for F q[T]. Inv. Math. 94,105–112 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  16. D. Thakur, Gamma functions for function fields and Drinfeld modules, To appear in Annals of Math.

    Google Scholar 

  17. D. Thakur, Gauss sums for function fields, To appear in Journal of Number Theory.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Francesco Baldassarri Siegfried Bosch Bernard Dwork

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this chapter

Cite this chapter

Thakur, D.S. (1990). Gross-Koblitz formula for function fields. In: Baldassarri, F., Bosch, S., Dwork, B. (eds) p-adic Analysis. Lecture Notes in Mathematics, vol 1454. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091149

Download citation

  • DOI: https://doi.org/10.1007/BFb0091149

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53477-8

  • Online ISBN: 978-3-540-46906-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics