Dirichlet character sums

Chunlei Liu

Acta Arithmetica (1999)

  • Volume: 88, Issue: 4, page 299-309
  • ISSN: 0065-1036

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Chunlei Liu. "Dirichlet character sums." Acta Arithmetica 88.4 (1999): 299-309. <http://eudml.org/doc/207248>.

@article{ChunleiLiu1999,
author = {Chunlei Liu},
journal = {Acta Arithmetica},
keywords = {exponential sums; Dirichlet characters},
language = {eng},
number = {4},
pages = {299-309},
title = {Dirichlet character sums},
url = {http://eudml.org/doc/207248},
volume = {88},
year = {1999},
}

TY - JOUR
AU - Chunlei Liu
TI - Dirichlet character sums
JO - Acta Arithmetica
PY - 1999
VL - 88
IS - 4
SP - 299
EP - 309
LA - eng
KW - exponential sums; Dirichlet characters
UR - http://eudml.org/doc/207248
ER -

References

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  1. [1] J.-R. Chen, On Professor Hua's estimate of exponential sums, Sci. Sinica 20 (1977), 711-719. Zbl0374.10024
  2. [2] P. Ding and M.-G. Qi, Further estimate of complete trigonometric sums, J. Tsinghua Univ. 29 (1989), no. 6, 74-85. Zbl0934.11038
  3. [3] C. F. Gauss, Summatio quarumdam serierum singularium, Comment. Soc. Reg. Sci. Gottingensis 1 (1811); Werke, Vol. 2, Königl. Gesellschaft der Wissenschaften, Göttingen, 1876, 9-45. 
  4. [4] G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio Numerorum': IV. The singular series in Waring's Problem and the value of the number G(k), Math. Z. 12 (1922), 161-188. Zbl48.0146.01
  5. [5] L.-K. Hua, On exponential sums, J. Chinese Math. Soc. 2 (1940), 301-312. Zbl0061.06608
  6. [6] L.-K. Hua, On exponential sums over an algebraic number field, Canad. J. Math. 3 (1951), 44-51. 
  7. [7] L.-K. Hua and H. S. Vandiver, On the existence of solutions of certain equations in a finite field, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 481-487. Zbl0034.01301
  8. [8] D. Ismoilov, Estimates of complete character sums of polynomials, Trudy Mat. Inst. Steklov. 200 (1991), 171-184 (in Russian). 
  9. [9] C. G. J. Jacobi, Brief an Gauss vom 8. Februar 1827, Gesammelte Werke, Vol. 7, Reimer, Berlin, 1891, 393-400. 
  10. [10] J.-L. Lagrange, Réflexions sur la résolution algébrique des équations, Nouv. Mémoires Acad. Roy. Berlin 1770, 134-215; Nouv. Mémoires Acad. Roy. Berlin 1771, 138-254; Oeuvres, Vol. 3, Gauthier-Villars, Paris, 1869, 205-421. 
  11. [11] M.-G. Lu, Estimate of a complete trigonometric sum, Sci. Sinica 28 (1985), 561-578. Zbl0599.10030
  12. [12] A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 204-207. Zbl0032.26102
  13. [13] A. Weil, Numbers of solutions of equations in finite fields, Bull. Amer. Math. Soc. 55 (1949), 497-508. Zbl0032.39402
  14. [14] A. Weil, La cyclotomie jadis et naguère, Enseign. Math. (2) 20 (1974), 247-263. 

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