The asymptotic distribution of Kloosterman sums

S. J. Patterson

Acta Arithmetica (1997)

  • Volume: 79, Issue: 3, page 205-219
  • ISSN: 0065-1036

How to cite

top

S. J. Patterson. "The asymptotic distribution of Kloosterman sums." Acta Arithmetica 79.3 (1997): 205-219. <http://eudml.org/doc/206976>.

@article{S1997,
author = {S. J. Patterson},
journal = {Acta Arithmetica},
keywords = {normalized eigenvalues; symmetric square; Kloosterman sums; power-residue symbols},
language = {eng},
number = {3},
pages = {205-219},
title = {The asymptotic distribution of Kloosterman sums},
url = {http://eudml.org/doc/206976},
volume = {79},
year = {1997},
}

TY - JOUR
AU - S. J. Patterson
TI - The asymptotic distribution of Kloosterman sums
JO - Acta Arithmetica
PY - 1997
VL - 79
IS - 3
SP - 205
EP - 219
LA - eng
KW - normalized eigenvalues; symmetric square; Kloosterman sums; power-residue symbols
UR - http://eudml.org/doc/206976
ER -

References

top
  1. [1] R. W. Bruggeman and R. J. Miatello, Estimates of Kloosterman sums for groups of real rank one, Duke Math. J. 80 (1995), 105-137. Zbl0866.11049
  2. [2] J. W. Cogdell and I. I. Piatetski-Shapiro, The Arithmetic and Spectral Analysis of Poincaré Series, Perspect. Math. 13, Academic Press, 1990. 
  3. [3] H. Davenport, On certain exponential sums, J. Reine Angew. Math. 169 (1933), 158-176. Zbl59.0370.03
  4. [4] W. Duke and H. Iwaniec, A relation between cubic exponential and Kloosterman sums, in: Contemp. Math. 143, Amer. Math. Soc., 1993, 255-258. Zbl0792.11029
  5. [5] T. Estermann, Vereinfachter Beweis eines Satzes von Kloosterman, Abh. Math. Sem. Hamburg 7 (1929), 82-98. Zbl55.0703.02
  6. [6] T. Estermann, On Kloosterman's sum, Mathematika 2 (1961), 83-86. Zbl0114.26302
  7. [7] Y. Z. Flicker, Automorphic forms on covering groups of GL(2), Invent. Math. 57 (1980), 119-182. Zbl0431.10014
  8. [8] I. M. Gel'fand, M. I. Graev and I. I. Piatetski-Shapiro, Representation Theory and Automorphic Functions, W. B. Saunders, 1969. 
  9. [9] D. Goldfeld and P. Sarnak, Sums of Kloosterman sums, Invent. Math. 71 (1983), 243-250. Zbl0507.10029
  10. [10] C. Hooley, On the distribution of the roots of polynomial congruences, Mathematika 11 (1964), 39-49. Zbl0123.25802
  11. [11] N. Katz, Gauss Sums , Kloosterman Sums and Monodromy Groups, Ann. of Math. Study 116, Princeton Univ. Press, 1988. Zbl0675.14004
  12. [12] D. A. Kazhdan and S. J. Patterson, Metaplectic forms, Publ. Math. I.H.E.S. 59 (1984), 35-142. Zbl0559.10026
  13. [13] H. D. Kloosterman, Asymptotische Formeln für die Fourierkoeffizienten ganzer Modulformen, Abh. Math. Sem. Hamburg 5 (1927), 337-352. Zbl53.0346.01
  14. [14] N. V. Kuznetsov, Peterson's hypothesis for parabolic forms of weight zero and Linnik's hypothesis. Sums of Kloosterman sums, Mat. Sb. 111 (1980), 334-383 (in Russian). Zbl0427.10016
  15. [15] S. Lang, Cyclotomic Fields, Grad. Texts in Math. 59, Springer, 1978. 
  16. [16] J. Lehner, Discontinuous Groups and Automorphic Functions, Amer. Math. Soc., 1964. Zbl0178.42902
  17. [17] A. V. Malyshev, Generalized Kloosterman sums and their applications, Vestnik Leningrad. Univ. 13 (1960), 59-75 (in Russian). 
  18. [18] I. Piatetski-Shapiro, Invariant theory and Kloosterman sums, in: Algebraic Groups, Proceedings of a Symposium in Utrecht, Lecture Notes in Math. 1271, Springer, 1987, 229-236. 
  19. [19] H. Salié, Zur Abschätzung der Fourierkoeffizienten ganzer Modulformen, Math. Z. 36 (1932), 263-278. Zbl58.0190.03
  20. [20] P. Sarnak, Additive number theory and Maass forms, in: Lecture Notes in Math. 1052, Springer, 1984, 286-309. 
  21. [21] G. Stevens, Poincaré series on GL(r) and Kloosterman sums, Math. Ann. 277 (1987), 25-51. Zbl0597.12017
  22. [22] G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge Univ. Press, 1944. Zbl0063.08184
  23. [23] A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 204-207 = Collected Papers, Vol. I, 1948, 386-389. 
  24. [24] D. J. Wright, Cubic character sums of cubic polynomials, Proc. Amer. Math. Soc. 100 (1987), 409-413. Zbl0624.10031

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.