广义二次Gauss和与广义Kloosterman和的混合均值
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摘要
利用分析的方法及经典二次Gauss和的性质,研究了一类广义二次Gauss和与广义Kloosterman和的混合均值的计算问题,并得到了一个精确的计算公式.
The main purpose of this paper is using the analytic method and the properties of the classical quadratic Gauss sums to study the computational problem of one kind hybrid power mean of the generalized quadratic Gauss sums and the generalized Kloosterman sums,and give an exact computational formula for it.
The main purpose of this paper is using the analytic method and the properties of the classical quadratic Gauss sums to study the computational problem of one kind hybrid power mean of the generalized quadratic Gauss sums and the generalized Kloosterman sums,and give an exact computational formula for it.
引文
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[2] Estermann T. On Kloostermann's sums[J]. Mathematica, 1961(8):83-86.
[3] Chowla S. On Kloosterman's sums[J]. Norkse Vid Selbsk Fak Frondheim, 1967(40):70-72.
[4] Malyshev A V. A generalization of Kloosterman sums and their estimates[J].(in Russian)Vestnik Leningrad University, 1960(15):59-75.
[5] Zhang W P. On the fourth power mean of the general Kloosterman sums[J]. Indian J Pure and Applied Mathematics, 2004(35):237-242.
[6] Li J H, and Liu Y N. Some new identities involving Gauss sums and general Kloosterman sums[J].Acta Mathematica Sinica(Chinese Series), 2013(56):413-416.
[7] Apostol T M. Introduction to Analytic Number Theory[M]. Springer-Verlag, New York, 1976.
[8] Hua L K. Introduction to Number Theory, Science Press, Beijing, 1979.
[9] Zhang W P, and Liu H N. On the general Gauss sums and their fourth power mean[J].Osaka Journal of Mathematics, 2005(42):189-199.
[10] Smith R A. On n-dimensional Kloostermann sums[J]. Journal of Number Theory, 1979(11):324-343.
[11] Luo W. Bounds for incomplete Kloostermann sums[J]. Journal of Number Theory, 1999(75):41-46.
[12] Shparlinski I E. Bounds of incomplete multiple Kloostermann sums, Journal of Number Theory,2007(126):68-73.
[13] Ye Y. Identities of incomplete Kloostermann sums[J]. Proc Amer Math Soc, 1999(127):2591-2600.
[14] Duke W, and Iwaniec H. A relation between cubic exponential and Kloosterman sums[J]. Contemporary Mathematics, 1993(143):255-258.
[15] Hulek K, Spandaw J, van Geemen B, and van Straten D. The modularity of the Barth-Nieto quintic and its relatives[J]. Adv Geom, 2001(1):263-289.
[16] Katz N M. Estimates for nonsingular multiplicative character sums[J]. International Mathematics Research Notices, 2002(7):333-349.
[17] Zhang H,and Zhang W P. The fourth power mean of two-term exponential sums and its application[J]. Mathematical Reports, 2017(19):75-81.
[18] Birch B J. How the number of points of an elliptic curve over a fixed prime field varies[J]. Journal of London Math Soc, 1968(43):57-60.
[2] Estermann T. On Kloostermann's sums[J]. Mathematica, 1961(8):83-86.
[3] Chowla S. On Kloosterman's sums[J]. Norkse Vid Selbsk Fak Frondheim, 1967(40):70-72.
[4] Malyshev A V. A generalization of Kloosterman sums and their estimates[J].(in Russian)Vestnik Leningrad University, 1960(15):59-75.
[5] Zhang W P. On the fourth power mean of the general Kloosterman sums[J]. Indian J Pure and Applied Mathematics, 2004(35):237-242.
[6] Li J H, and Liu Y N. Some new identities involving Gauss sums and general Kloosterman sums[J].Acta Mathematica Sinica(Chinese Series), 2013(56):413-416.
[7] Apostol T M. Introduction to Analytic Number Theory[M]. Springer-Verlag, New York, 1976.
[8] Hua L K. Introduction to Number Theory, Science Press, Beijing, 1979.
[9] Zhang W P, and Liu H N. On the general Gauss sums and their fourth power mean[J].Osaka Journal of Mathematics, 2005(42):189-199.
[10] Smith R A. On n-dimensional Kloostermann sums[J]. Journal of Number Theory, 1979(11):324-343.
[11] Luo W. Bounds for incomplete Kloostermann sums[J]. Journal of Number Theory, 1999(75):41-46.
[12] Shparlinski I E. Bounds of incomplete multiple Kloostermann sums, Journal of Number Theory,2007(126):68-73.
[13] Ye Y. Identities of incomplete Kloostermann sums[J]. Proc Amer Math Soc, 1999(127):2591-2600.
[14] Duke W, and Iwaniec H. A relation between cubic exponential and Kloosterman sums[J]. Contemporary Mathematics, 1993(143):255-258.
[15] Hulek K, Spandaw J, van Geemen B, and van Straten D. The modularity of the Barth-Nieto quintic and its relatives[J]. Adv Geom, 2001(1):263-289.
[16] Katz N M. Estimates for nonsingular multiplicative character sums[J]. International Mathematics Research Notices, 2002(7):333-349.
[17] Zhang H,and Zhang W P. The fourth power mean of two-term exponential sums and its application[J]. Mathematical Reports, 2017(19):75-81.
[18] Birch B J. How the number of points of an elliptic curve over a fixed prime field varies[J]. Journal of London Math Soc, 1968(43):57-60.