Math.ExpPairs.Ivic

Provides functions to compute estimates Riemann zeta-function ζ in a critical strip, given in Ivić A. `The Riemann zeta-function: Theory and applications', Mineola, New York: Dover Publications, 2003.

Documentation

zetaOnS :: Rational -> OptimizeResult

Compute µ(σ) such that |ζ(σ+it)| ≪ |t|^µ(σ) . See equation (7.57) in Ivić2003.

reverseZetaOnS :: Rational -> OptimizeResult

An attempt to reverse zetaOnS.

mOnS :: Rational -> OptimizeResult

Compute m(σ) such that ∫_1^T |ζ(σ+it)|^m(σ) dt ≪ T^(1+ε) See equation (8.97) in Ivić2003.