On the Hybrid Power Mean Involving the Two-Term Exponential Sums and Polynomial Character Sums

Xingxing Lv; Xiaoxue Li

doi:10.1007/s11401-020-0216-7

Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (4) : 547 -558. DOI: 10.1007/s11401-020-0216-7

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On the Hybrid Power Mean Involving the Two-Term Exponential Sums and Polynomial Character Sums

Xingxing Lv ¹^,^a
, Xiaoxue Li ²^,^b

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Abstract

The main purpose of this paper is using the analytic method and the properties of trigonometric sums and character sums to study the computational problem of one kind hybrid power mean involving two-term exponential sums and polynomial character sums. Then the authors give some interesting calculating formulae for them.

Keywords

The two-term exponential sums / Kloosterman sums / Dirichlet character of polynomials / Hybrid power mean / Identity

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Xingxing Lv, Xiaoxue Li. On the Hybrid Power Mean Involving the Two-Term Exponential Sums and Polynomial Character Sums. Chinese Annals of Mathematics, Series B, 2020, 41(4): 547-558 DOI:10.1007/s11401-020-0216-7

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References

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[1]	Apostol T M. Introduction to Analytic Number Theory, 1976, New York: Springer-Verlag

[2]	Han D. A hybrid mean value involving two-term exponential sums and polynomial character sums. Czechoslovak Mathematical Journal, 2014, 64: 53-62

[3]	Du X Y. The hybrid power mean of two-term exponential sums and character sums. Acta Mathematica Sinica (Chinese Series), 2016, 59: 309-316

[4]	Cochrane T, Pinner C. Using Stepanov’s method for exponential sums involving rational functions. Journal of Number Theory, 2006, 116: 270-292

[5]	Estermann T. On Kloostermann’s sums. Mathematica, 1961, 8: 83-86

[6]	Chowla S. On Kloosterman’s sums. Norkse Vid. Selbsk. Fak. Frondheim, 1967, 40: 70-72

[7]	Zhang W P, Yi Y. On Dirichlet characters of polynomials. Bulletin of the London Mathematical Society, 2002, 34: 469-473

[8]	Zhang W P, Yao W L. A note on the Dirichlet characters of polynomials. Acta Arithmetica, 2004, 115: 225-229

[9]	Zhang W P, Han D. On the sixth power mean of the two-term exponential sums. Journal of Number Theory, 2014, 136: 403-413

[10]	Zhang W P. The fourth and sixth power mean of the classcial Kloosterman sums. Journal of Number Theory, 2011, 131: 228-238

[11]	Zhang W P. On the fourth power mean of the general Kloosterman sums. Indian Journal of Pure and Applied Mathematics, 2004, 35: 237-242

[12]	Katz N M. Estimates for nonsingular multiplicative character sums. International Mathematics Research Notices, 2002, 7: 333-349

[13]	Li J H, Liu Y N. Some new identities involving Gauss sums and general Kloosterman sums. Acta Mathematica Sinica (Chinese Series), 2013, 56: 413-416