Dirichlet character sums
Chunlei Liu
Acta Arithmetica, Tome 89 (1999), p. 299-309 / Harvested from The Polish Digital Mathematics Library
Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:207248
@article{bwmeta1.element.bwnjournal-article-aav88i4p299bwm,
     author = {Chunlei Liu},
     title = {Dirichlet character sums},
     journal = {Acta Arithmetica},
     volume = {89},
     year = {1999},
     pages = {299-309},
     zbl = {0931.11029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav88i4p299bwm}
}
Chunlei Liu. Dirichlet character sums. Acta Arithmetica, Tome 89 (1999) pp. 299-309. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav88i4p299bwm/

[000] [1] J.-R. Chen, On Professor Hua's estimate of exponential sums, Sci. Sinica 20 (1977), 711-719. | Zbl 0374.10024

[001] [2] P. Ding and M.-G. Qi, Further estimate of complete trigonometric sums, J. Tsinghua Univ. 29 (1989), no. 6, 74-85. | Zbl 0934.11038

[002] [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.

[003] [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. | Zbl 48.0146.01

[004] [5] L.-K. Hua, On exponential sums, J. Chinese Math. Soc. 2 (1940), 301-312. | Zbl 0061.06608

[005] [6] L.-K. Hua, On exponential sums over an algebraic number field, Canad. J. Math. 3 (1951), 44-51.

[006] [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. | Zbl 0034.01301

[007] [8] D. Ismoilov, Estimates of complete character sums of polynomials, Trudy Mat. Inst. Steklov. 200 (1991), 171-184 (in Russian).

[008] [9] C. G. J. Jacobi, Brief an Gauss vom 8. Februar 1827, Gesammelte Werke, Vol. 7, Reimer, Berlin, 1891, 393-400.

[009] [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.

[010] [11] M.-G. Lu, Estimate of a complete trigonometric sum, Sci. Sinica 28 (1985), 561-578. | Zbl 0599.10030

[011] [12] A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 204-207. | Zbl 0032.26102

[012] [13] A. Weil, Numbers of solutions of equations in finite fields, Bull. Amer. Math. Soc. 55 (1949), 497-508. | Zbl 0032.39402

[013] [14] A. Weil, La cyclotomie jadis et naguère, Enseign. Math. (2) 20 (1974), 247-263.