Totient Dirichlet series and its absolute convergence boundary
ID: totient-dirichlet-series-and-its-absolute-convergence-boundary
The totient divisor-sum identity and multiplication of absolutely convergent Dirichlet series give the quotient for . The bound proves convergence there. The simple pole of the Riemann zeta function at one makes the quotient unbounded as real . Since the coefficients are nonnegative, convergence at two would bound all these larger-real-part values, a contradiction. Thus the abscissa of absolute convergence of a Dirichlet series is two.
New to topics? Read the docs here!