Copyright | (c) Andrew Lelechenko 2014-2015 |
---|---|
License | GPL-3 |
Maintainer | andrew.lelechenko@gmail.com |
Stability | experimental |
Portability | POSIX |
Safe Haskell | None |
Language | Haskell2010 |
Provides a set of initial exponent pairs, consisting of two points (0, 1), (1/2, 1/2) and a triangle with vertices in (1/6, 2/3), (2/13, 35/52) and (32/205, 269/410). The triangle is represented as a list of nodes of a net, covering the triangle.
Below A and B stands for van der Corput's processes. See Math.ExpPairs.Process for explanations.
Documentation
Vertices of the triangle of initial exponent pairs.
Corput16 | Usual van der Corput exponent pair (1/6, 2/3) = AB(0, 1). |
HuxW87b1 | An exponent pair (2/13, 35/52) from Huxley M. N. `Exponential sums and the Riemann zeta function' // Proceedings of the International Number Theory Conference held at Universite Laval in 1987, Walter de Gruyter, 1989, P. 417-423. |
Hux05 | An exponent pair (32/205, 269/410) from Huxley M. N. `Exponential sums and the Riemann zeta function V' // Proc. Lond. Math. Soc., 2005, Vol. 90, no. 1., P. 1--41. |
Type to hold an initial exponent pair.
initPairToValue :: InitPair -> (Rational, Rational) Source #
Convert initial exponent pair from its symbolic representation
as InitPair
to pair of rationals.
initPairToProjValue :: InitPair -> (Integer, Integer, Integer) Source #
Same as initPairToValue
, but immediately convert from Q^2 to PN^3.