Description

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This book is the second of two books in a series by the author on the generalized Riemann hypothesis. The Euler-Maclaurin summation formula, the Borel integral summation method, the Euler reflection formula for the gamma function, and the result of the first book of this series are used to prove that all roots of Dirichlet L-functions with principal characters in the critical strip are identical to the roots of the Riemann zeta function, and therefore have real part equal to 1/2. Furthermore, the Euler-Maclaurin summation formula, the Borel integral summation method, bi-lateral integral transform representations of the partial sums of the Dirichlet L-functions with non-principal characters in the critical strip, and the generalized functional equation of the Dirichlet L-functions are used to prove that all roots of the Dirichlet L-functions with non-principal characters in the critical strip have real part equal to 1/2.