参考文献:1.Bae S., Cha B., Jung H.: M枚bius function in short intervals for function fields. Finite Fields Appl. 34, 235鈥?49 (2015)MathSciNet CrossRef 2.Carlitz L.: The arithmetic of polynomials in a Galois field. Amer. J. Math. 54, 39鈥?0 (1932)MathSciNet CrossRef 3.Carmon D., Rudnick Z.: The autocorrelation of the M枚bius function and Chowlas conjecture for the rational function field. Quart. J. Math. 65, 53鈥?1 (2014)MathSciNet CrossRef MATH 4.Dalen K.: On a theorem of Stickelberger. Math. Scand. 3, 124鈥?26 (1955)MathSciNet MATH 5.Deligne P.: La conjecture de Weil, I. Inst. Hautes Etudes Sci. Publ. Math. 43, 273鈥?07 (1974)MathSciNet CrossRef 6.Deligne P.: La conjecture de Weil, II. Inst. Hautes Etudes Sci. Publ. Math. 52, 313鈥?28 (1981) 7.M. Drmota and R. F. Tichy, Sequences, discrepancies and applications, Springer-Verlag, Berlin, 1997. 8.I. M. Gelfand, M. M. Kapranov and A. V. Zelevinsky, Discriminants, resultants, and multidimensional determinants, Birkh盲user, Boston 1994. 9.D. G贸mez-P茅rez et聽al. Stable polynomials over finite fields, Rev. Mat. Iberoam. (to appear). 10.Granville A., Soundararajan K.: Large character sums. J. Amer. Math. Soc. 14, 365鈥?97 (2001)MathSciNet CrossRef MATH 11.G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford Univ. Press, Oxford, 1979. 12.H. Iwaniec and E. Kowalski, Analytic number theory, Amer. Math. Soc., Providence, RI, 2004. 13.Katz N. M.: Estimates for 鈥渟ingular鈥?exponential sums. Intern. Math. Res. Notices 16, 875鈥?99 (1999)CrossRef 14.Katz N.M.: Estimates for nonsingular multiplicative character sums. Intern. Math. Res. Notices 2002, 333鈥?49 (2002)CrossRef MATH 15.Katz N. M.: Estimates for nonsingular mixed character sums. Intern. Math. Res. Notices 2007, 1鈥?9 (2007) 16.Katz N. M.: Estimates for mixed character sums. Geom. Funct. Anal., 18, 1251鈥?269 (2008)MathSciNet CrossRef MATH 17.L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Wiley-Interscience, New York-London-Sydney, 1974. 18.W.-C. W. Li, Number theory with applications, World Scientific, Singapore, 1996. 19.R. Lidl and H. Niederreiter, Finite Fields, Cambridge Univ. Press, Cambridge, 1997. 20.H. L. Montgomery, Ten lectures on the interface between analytic number theory and harmonic analysis, Amer. Math. Soc., Providence, RI, 1994. 21.Montgomery H. L., Vaughan R. C.: Exponential sums with multiplicative coefficients. Invent. Math. 43, 69鈥?2 (1977)MathSciNet CrossRef MATH 22.Rojas-Le贸n A.: Estimates for singular multiplicative character sums. Intern. Math. Res. Notices 2005, 1221鈥?234 (2005)CrossRef MATH 23.L. Stickelberger, 脺ber eine neue Eigenschaft der Diskriminanten algebraischer Zahlk枚rper, Verh. 1 Internat. Math. Kongresses, 1897, Leipzig, 1898, 182鈥?93.
作者单位:Igor E. Shparlinski (1)
1. Department of Pure Mathematics, University of New South Wales, Sydney, NSW, 2052, Australia
刊物类别:Mathematics and Statistics
刊物主题:Mathematics Mathematics
出版者:Birkh盲user Basel
ISSN:1420-8938
文摘
We obtain bounds of sums of additive characters with discriminants of polynomials over finite fields. We use these bounds to study the distribution of discriminants modulo a prime p. Mathematics Subject Classification 11T06 11T23