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On Exponential Sums Involving the Ideal Counting Function in Quadratic Number Fields

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Abstract.

 Let χ be a Dirichlet character modulo k > 1, and F χ(n) the arithmetical function which is generated by the product of the Riemann zeta-function and the Dirichlet L-function corresponding to χ in . In this paper we study the asymptotic behaviour of the exponential sums involving the arithmetical function F χ(n). In particular, we study summation formulas for these exponential sums and mean square formulas for the error term.

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  1. Nagoya University, Japan, , , , , , JP

    Jun Furuya

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  1. Jun Furuya
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Received April 17, 2001; in revised form April 2, 2002

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Furuya, J. On Exponential Sums Involving the Ideal Counting Function in Quadratic Number Fields. Monatsh. Math. 137, 129–156 (2002). https://doi.org/10.1007/s00605-002-0495-y

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  • DOI: https://doi.org/10.1007/s00605-002-0495-y

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