Sommes de Gauss cubiques et revêtements de S L ( 2 )

P. Deligne

Séminaire Bourbaki (1978-1979)

  • Volume: 21, page 244-277
  • ISSN: 0303-1179

How to cite

top

Deligne, P.. "Sommes de Gauss cubiques et revêtements de $SL(2)$." Séminaire Bourbaki 21 (1978-1979): 244-277. <http://eudml.org/doc/109940>.

@article{Deligne1978-1979,
author = {Deligne, P.},
journal = {Séminaire Bourbaki},
keywords = {Kummer's conjecture; uniform distribution; cubic Gaussian sums; cubic theta series; representation theory of metaplectic groups},
language = {fre},
pages = {244-277},
publisher = {Springer-Verlag},
title = {Sommes de Gauss cubiques et revêtements de $SL(2)$},
url = {http://eudml.org/doc/109940},
volume = {21},
year = {1978-1979},
}

TY - JOUR
AU - Deligne, P.
TI - Sommes de Gauss cubiques et revêtements de $SL(2)$
JO - Séminaire Bourbaki
PY - 1978-1979
PB - Springer-Verlag
VL - 21
SP - 244
EP - 277
LA - fre
KW - Kummer's conjecture; uniform distribution; cubic Gaussian sums; cubic theta series; representation theory of metaplectic groups
UR - http://eudml.org/doc/109940
ER -

References

top
  1. [1] I.N. Bernstein and A.V. Zelevinsky - Representations of the group GL(n,F), where F is a local non archimedian field - Uspekhi Math. Nauk.313 (1976) p 5-70. Zbl0348.43007MR425030
  2. [2] I.N. Bernstein and A.V. Zelevinsky - Induced representations of reductive p-adic groups I - Ann. Sc. ENS10 (1977) p 441-472. Zbl0412.22015MR579172
  3. [3] Y. Flicker - Automorphic forms on covering groups of GL(2) - preprint IAS. 
  4. [4] B. Gross and N. Koblitz - Gauss sums and the p-adic Γ-function. Zbl0406.12010
  5. [5] D.R. Heath-Brown and S.J. Patterson - The distribution of Kummer sums at prime arguments. Zbl0412.10028
  6. [6] H. Jacquet and R.P. Langlands - Automorphic forms on GL(2) - Springer Lecture Notes. 114 (1970). Zbl0236.12010MR401654
  7. [7] T. Kubota - On automorphic functions and the reciprocity law in a number field - Lectures Notes in Math.2, Kyoto Univ.1969. Zbl0231.10017MR255490
  8. [8] T. Kubota - Some results concerning reciprocity law and real analytic automorphic functions. Proc. Symp. Pure Math.20 (1971) p 382-395. Zbl0215.36103MR340221
  9. [9] T. Kubota - Some number theoretical resuits on real analytic automorphic forms - Several complex variables, Maryland (1970). Springer Lecture Notes185 p 87-96. Zbl0212.06901MR314768
  10. [10] T. Kubota - On an analogy to the Poisson summation formula for generaiized Fourier transforms - J. Crelle268 (1974) p 180-189. Zbl0286.12007MR352051
  11. [11] T. Kubota - Elementary theory of Eisenstein series - Kodanska1973. Zbl0268.10012MR429749
  12. [12] R.P. Langlands - On the functional equations satisfied by Eisenstein series - Springer Lecture Notes544. Zbl0332.10018MR579181
  13. [13] C.R. Matthews - Gauss sums and eiliptic functions - I the Kummer sum, Inv. Math522(1979) p163-186; II the quartic sum. Preprint IHES. Zbl0388.10025MR536079
  14. [14] H. Matsumoto - Sur les sous-groupes arithmétiques des groupes semi-simples déployés - Ann. Sc. ENS2 (1969) p 1-62. Zbl0261.20025MR240214
  15. [15] J. Milnor - Algebraic K-theory and quadratic forms - Inv. Math. (1970) p 318-344. Zbl0199.55501MR260844
  16. [16] C. Moen - Intertwining operators for covering groups of SL(2) over a local field. Thesis. University of Chicago1979. 
  17. [17] C. Moore - Group extensions of p-adic and adelic linear groups - Publ. Math. IHES35 (1968) p 5-70. Zbl0159.03203MR244258
  18. [18] S.J. Patterson - A cubic analogue of the theta series - I,II - J. Crelle296 (1977) p 125-161 et 217-220. Zbl0358.10012MR563068
  19. [19] S.J. Patterson - On the distribution of Kummer sums - J. Crelle303/304 (1978) p 126-143. Zbl0384.10017MR514676
  20. [20] S.J. Patterson - On Dirichlet series associated with cubic Gauss sums - J. Crelle303/304 (1978) p 102-125. Zbl0384.10016MR514675
  21. [21] J.P. Serre - Corps locaux - Pubi. Ins. Math. Univ. Nancago VIII - Hermann1962. Zbl0137.02601MR354618
  22. [22] A. Weil - Jacobi sums as "grössencharaktere" - Trans. AMS73 (1952) p487-495. Zbl0048.27001MR51263
  23. [23] A. Weil - Dirichiet series and automorphic forms - Springer Lecture Note189 (1971). Zbl0218.10046
  24. [24] Algebraic K-theory I,II,III - Springer Lecture Notes341, 342, 343. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.