Abstract:We provide efficient methods to evaluate the Riemann zeta, the Lerch zeta and the Dirichlet L-functions. The method uses the Riemann-Siegel (RS) type formulas and a modified double exponential (MDE) quadrature method near the saddle point of appropriate integrands. We provide simplified derivations of the RS formulas, containing finite series sums and residual integrals, for the Lerch and the Dirichlet L-functions. The MDE method allows us to remove the contribution of the singularities near the contour of int… Show more
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