Hyper-Kloosterman sums and estimation of exponential sums of polynomials of higher degrees

Yangbo Ye

Acta Arithmetica (1998)

  • Volume: 86, Issue: 3, page 255-267
  • ISSN: 0065-1036

How to cite

top

Yangbo Ye. "Hyper-Kloosterman sums and estimation of exponential sums of polynomials of higher degrees." Acta Arithmetica 86.3 (1998): 255-267. <http://eudml.org/doc/207195>.

@article{YangboYe1998,
author = {Yangbo Ye},
journal = {Acta Arithmetica},
keywords = {Kloosterman sums; estimation of exponential sums},
language = {eng},
number = {3},
pages = {255-267},
title = {Hyper-Kloosterman sums and estimation of exponential sums of polynomials of higher degrees},
url = {http://eudml.org/doc/207195},
volume = {86},
year = {1998},
}

TY - JOUR
AU - Yangbo Ye
TI - Hyper-Kloosterman sums and estimation of exponential sums of polynomials of higher degrees
JO - Acta Arithmetica
PY - 1998
VL - 86
IS - 3
SP - 255
EP - 267
LA - eng
KW - Kloosterman sums; estimation of exponential sums
UR - http://eudml.org/doc/207195
ER -

References

top
  1. [1] L. Carlitz and S. Uchiyama, Bounds for exponential sums, Duke Math. J. 24 (1957), 37-41. Zbl0088.03901
  2. [2] R. Dąbrowski and B. Fisher, A stationary phase formula for exponential sums over / p m and applications to GL(3)-Kloosterman sums, Acta Arith. 80 (1997), 1-48. Zbl0893.11032
  3. [3] H. Davenport und H. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen, J. Reine Angew. Math. 172 (1935), 151-182. Zbl60.0913.01
  4. [4] P. Deligne, Applications de la formule des traces aux sommes trigonométriques, in: Cohomologie Etale (SGA 4 1/2), Lecture Notes in Math. 569, Springer, Berlin, 1977, 168-232. 
  5. [5] L. K. Hua, On exponential sums, J. Chinese Math. Soc. 2 (1940), 301-312. Zbl0061.06608
  6. [6] N. M. Katz, Sommes exponentielles, Astérisque 79 (1980). 
  7. [7] N. M. Katz, Gauss Sums, Kloosterman Sums, and Monodromy Groups, Ann. of Math. Stud. 116, Princeton Univ. Press, Princeton, 1988. Zbl0675.14004
  8. [8] N. M. Katz, Exponential Sums and Differential Equations, Ann. of Math. Stud. 124, Princeton Univ. Press, Princeton, 1990. Zbl0731.14008
  9. [9] J. H. Loxton and R. A. Smith, On Hua's estimate for exponential sums, J. London Math. Soc. 26 (1982), 15-20. Zbl0474.10030
  10. [10] J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985), 440-454. Zbl0575.10033
  11. [11] R. C. Vaughan, The Hardy-Littlewood Method, 2nd ed., Cambridge Tracts in Math. 125, Cambridge Univ. Press, Cambridge, 1997. Zbl0868.11046
  12. [12] Y. Ye, The lifting of an exponential sum to a cyclic algebraic number field of a prime degree, Trans. Amer. Math. Soc., to appear. Zbl0922.11068

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.