多项式的特征和及其L-函数

张佳凡, 吕星星

数学学报 ›› 2019, Vol. 62 ›› Issue (6) : 903-912.

PDF(409 KB)
PDF(409 KB)
数学学报 ›› 2019, Vol. 62 ›› Issue (6) : 903-912. DOI: 10.12386/A2019sxxb0081
论文

多项式的特征和及其L-函数

    张佳凡, 吕星星
作者信息 +

On the Character Sums of Polynomials and L-functions

    Jia Fan ZHANG, Xing Xing LV
Author information +
文章历史 +

摘要

本文使用解析方法及特征和的性质研究了一类多项式的特征和与模p的狄利克莱L-函数的混合幂均值的计算问题,并给出了它们的一些计算公式.

Abstract

The main purpose of this paper is using the analytic methods and the properties of character sums to study the computational problem of one kind hybrid power mean involving the character sums of polynomials and Dirichlet L-functions modulo p, an odd prime, and give some exact computational formulas for them.

关键词

狄利克莱L-函数 / 多项式的特征和 / 混合幂均值 / 解析方法 / 计算公式

Key words

Dirichlet L-functions / character sums of polynomials / hybrid power mean / analytic method / computational formula

引用本文

导出引用
张佳凡, 吕星星. 多项式的特征和及其L-函数. 数学学报, 2019, 62(6): 903-912 https://doi.org/10.12386/A2019sxxb0081
Jia Fan ZHANG, Xing Xing LV. On the Character Sums of Polynomials and L-functions. Acta Mathematica Sinica, Chinese Series, 2019, 62(6): 903-912 https://doi.org/10.12386/A2019sxxb0081

参考文献

[1] Apostol Tom M., Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
[2] Bourgain J., Garaev M. Z., Konyagin S. V., et al., On the hidden shifted power problem, SIAM J. Comput., 2012, 41:1524-1557.
[3] Burgess D. A., On character sums and primitive roots, Proc. London Math. Soc., 1962, 12:179-192.
[4] Burgess D. A., On Dirichlet characters of polynomials, Proc. London Math. Soc., 1963, 13:537-548.
[5] Granville A., Soundararajan K., Large character sums:Pretentious characters and the Pólya-Vinogradov theorem, J. Amer. Math. Soc., 2007, 20:357-384.
[6] Ireland K., Rosen M., A Classical Introduction to Modern Number Theory, Springer-Verlag, New York, 1982.
[7] Pan C. D., Pan C. B., Goldbach Conjecture, Science Press, Beijing, 1992.
[8] Walum H., An exact formula for an average of L-series, Illinois Journal of Mathematics, 1982, 26:1-3.
[9] Weil A., On some exponential sums, Proc. Nat. Acad. Sci. U.S.A., 1948, 34:203-210.
[10] Zhang W. P., On the mean value of L-functions with the weight of character sums, Journal of Number Theory, 2008, 128:2459-2466.
[11] Zhang W. P., Moments of Generalized Quadratic Gauss Sums Weighted by L-Functions, Journal of Number Theory, 2002, 92:304-314.
[12] Zhang W. P., Lecture Notes in Contemporary Mathematics, Science Press, Beijing, 1989:173-179.
[13] Zhang W. P., On the mean values of Dedekind Sums, Journal de Théorie des Nombres de Bordeaux, 1996, 8:429-442.
[14] Zhang W. P., Yao W. L., A note on the Dirichlet characters of polynomials, Acta Arith., 2004, 115:225-229.
[15] Zhang W. P., Yi Y., On Dirichlet characters of polynomials, Bull. London Math. Soc., 2002, 34:469-473.
[16] Zhang W. P., Yi Y., He X. L., On the 2k-th Power Mean of Dirichlet L-Functions with the Weight of General Kloosterman Sums, Journal of Number Theory, 2000, 84:199-213.

基金

国家自然科学基金资助项目(11771351)

PDF(409 KB)

676

Accesses

0

Citation

Detail

段落导航
相关文章

/