Abstract
Let q be an odd prime, χ be a non-principal Dirichlet character modq and L(s,χ) be the associated Dirichlet L-function. For every odd prime q≤107, we show that L(1,χ□)>c1logq and β<1−c2logq, where c1=0.0124862668…, c2=0.0091904477…, χ□ is the quadratic Dirichlet character modq and β∈(0,1) is the Landau-Siegel zero, if it exists, of the set of such Dirichlet L-functions. As a by-product of the computations here performed, we also obtained some information about Littlewood's and Joshi's bounds on L(1,χ□) and on the class number of the imaginary quadratic field Q(−q).
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