Estimates for L-functions in the critical strip under GRH with effective applications
Abstract
Assuming the Generalized Riemann Hypothesis, we provide explicit upper bounds for moduli of L(s) and L'(s)/L(s) in the neighbourhood of the 1-line when L(s) are the Riemann, Dirichlet and Dedekind zeta-functions. To do this, we generalize Littlewood's well known conditional result to functions in the Selberg class with a polynomial Euler product, for which we also establish a suitable convexity estimate. As an application we provide conditional and effective estimate for the Mertens function.
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