Copyright | (c) Andrew Lelechenko, 2014-2015 |
---|---|
License | GPL-3 |
Maintainer | andrew.lelechenko@gmail.com |
Stability | experimental |
Portability | POSIX |
Safe Haskell | None |
Language | Haskell2010 |
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.
- zetaOnS :: Rational -> OptimizeResult
- reverseZetaOnS :: Rational -> OptimizeResult
- mOnS :: Rational -> OptimizeResult
Documentation
zetaOnS :: Rational -> OptimizeResult Source
Compute µ(σ) such that |ζ(σ+it)| ≪ |t|^µ(σ) . See equation (7.57) in Ivić2003.
reverseZetaOnS :: Rational -> OptimizeResult Source
An attempt to reverse zetaOnS
.
mOnS :: Rational -> OptimizeResult Source
Compute m(σ) such that ∫_1^T |ζ(σ+it)|^m(σ) dt ≪ T^(1+ε). See equation (8.97) in Ivić2003.