On some hybrid power moments of products of generalized quadratic Gauss sums and Kloosterman sums. (English) Zbl 1429.11146
Summary: In this paper, we investigate hybrid power moments of generalized quadratic Gauss sums weighted with powers of Kloosterman sums and with powers of values of Dirichlet \(L\)-functions at 1. We obtain several exact formulas for prime and prime power modulus and some asymptotic formulas.
MSC:
| 11L05 | Gauss and Kloosterman sums; generalizations |
| 11T24 | Other character sums and Gauss sums |
| 11M20 | Real zeros of \(L(s, \chi)\); results on \(L(1, \chi)\) |
Keywords:
generalized quadratic Gauss sums; Kloosterman sums; hybrid power mean values; Dirichlet \(L\)-functionsReferences:
| [1] | H. Iwaniec and E. Kowalski, Analytic Number Theory, Colloq. Publ., Am.Math. Soc., Vol. 53, AMS, Providence, RI, 2004. · Zbl 1059.11001 |
| [2] | S. Kanemitsu, Y. Tanigawa, M. Yoshimoto, and W. Zhang, On the discrete mean square of the Dirichlet L-functions at 1, Math. Z., 248(1):21-44, 2004. · Zbl 1133.11051 · doi:10.1007/s00209-004-0651-2 |
| [3] | X. Lv and W. Zhang, A new hybrid power mean involving the generalized quadratic Gauss sums and sums analogous to Kloosterman sums, Lith. Math. J., 57(3):359-366, 2017. · Zbl 1373.11060 · doi:10.1007/s10986-017-9366-z |
| [4] | H. Montgomery and R. Vaughan, Multiplicative Number Theory I. Classical Theory, Camb. Stud. Adv. Math., Vol. 97, Cambridge Univ. Press, Cambridge, 2006. · Zbl 1245.11002 |
| [5] | S. Walum, An exact formula for an average of L-series, Ill. J. Math., 26:1-3, 1982. · Zbl 0464.10030 |
| [6] | W. Zhang, Moments of generalized quadratic Gauss sums weighted by L-functions, J. Number Theory, 92(2):304-314, 2002. · Zbl 0997.11064 · doi:10.1006/jnth.2001.2715 |
| [7] | W. Zhang and R. Duan, On the mean square value of L-functions with the weight of quadratic Gauss sums, J. Number Theory, 179:77-87, 2017. · Zbl 1418.11122 · doi:10.1016/j.jnt.2017.03.019 |
| [8] | W. Zhang, Y. Yi, and X. He, On the 2k-th power mean of Dirichlet L-functionswith the weight of general Kloosterman sums, J. Number Theory, 84(2):199-213, 2000. · Zbl 0958.11061 · doi:10.1006/jnth.2000.2515 |
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