Abstract.
In this note, we prove an inversion formula for Dirichlet polynomials involving a non-principal character. By using Heath-Brown's upper-bound for Dirichlet's L-functions, we are able to obtain a non-trivial upper-bound for the error term in the q aspect. As an application we obtain an approximate functional equation for Dirichlet's L-functions to the right of the critical line with a sharp error term.
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Received: 27.12.1996
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Wang, W. Inversion formula of Dirichlet polynomials and the approximate functional equation of Dirichlet's L-functions. Arch. Math. 69, 305–312 (1997). https://doi.org/10.1007/s000130050125
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DOI: https://doi.org/10.1007/s000130050125