Copyright | (c) Andrew Lelechenko 2014-2015 |
---|---|
License | GPL-3 |
Maintainer | andrew.lelechenko@gmail.com |
Stability | experimental |
Portability | POSIX |
Safe Haskell | Safe |
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. |
Bourgain17 | An exponent pair (13/84, 55/84) from Bourgain J. `Decoupling, exponential sums and the Riemann zeta function` // J. Amer. Math. Soc., 2017, 30, P. 205-224. |
Instances
Bounded Triangle Source # | |
Enum Triangle Source # | |
Eq Triangle Source # | |
Ord Triangle Source # | |
Defined in Math.ExpPairs.Pair | |
Show Triangle Source # | |
Generic Triangle Source # | |
Pretty Triangle Source # | |
Defined in Math.ExpPairs.Pair | |
type Rep Triangle Source # | |
Defined in Math.ExpPairs.Pair |
Type to hold an initial exponent pair.
Corput01 | Usual van der Corput exponent pair (0, 1). |
Corput12 | Usual van der Corput exponent pair (1/2, 1/2) = B(0, 1). |
Mix !t !t | Point from the interior of |
Instances
Eq t => Eq (InitPair' t) Source # | |
Ord t => Ord (InitPair' t) Source # | |
Defined in Math.ExpPairs.Pair | |
Show t => Show (InitPair' t) Source # | |
Generic (InitPair' t) Source # | |
(Pretty t, Num t, Eq t) => Pretty (InitPair' t) Source # | |
Defined in Math.ExpPairs.Pair | |
type Rep (InitPair' t) Source # | |
Defined in Math.ExpPairs.Pair type Rep (InitPair' t) = D1 (MetaData "InitPair'" "Math.ExpPairs.Pair" "exp-pairs-0.2.0.0-KHgC3bMWFtS3BpPTx68RIa" False) (C1 (MetaCons "Corput01" PrefixI False) (U1 :: * -> *) :+: (C1 (MetaCons "Corput12" PrefixI False) (U1 :: * -> *) :+: C1 (MetaCons "Mix" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 t) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 t)))) |
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.