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- W2024804933 abstract "The main purpose of the paper is to study, using the analytic method and the property of the Ramanujan’s sum, the computational problem of the mean value of the mixed exponential sums with Dirichlet characters and general Gauss sum. For integers m, n, k, q, with k ⩾ 1 and q ⩾ 3, and Dirichlet characters χ, χ̄ modulo q we define a mixed exponential sum $$C(m,n;k;chi ;overline chi ;q) = sumlimits_{a = 1}^q {chi (a){G_k}(a,overline chi )eleft( {{{m{a^k} + noverline {{a^k}} } over q}} right)} ,$$ , with Dirichlet character χ and general Gauss sum G k (a, χ̄) as coefficient, where Σ′ denotes the summation over all a such that (a, q) = 1, aā ≡ 1 mod q and e(y) = e2πiy . We mean value of $$sumlimits_m {sumlimits_chi {sumlimits_{overline chi } {C{{left| {m,n;k;chi ;overline chi ;q} right|}^4}} } } ,$$ , and give an exact computational formula for it." @default.
- W2024804933 created "2016-06-24" @default.
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- W2024804933 date "2013-06-01" @default.
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- W2024804933 title "On the mean value of the mixed exponential sums with Dirichlet characters and general gauss sum" @default.
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- W2024804933 doi "https://doi.org/10.1007/s10587-013-0030-4" @default.
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