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Results tagged with computational-number-theory
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user 5267
Computational Number Theory is for explicit calculations or algorithms involving anything of interest to number theorists.
27
votes
Accepted
Open project: Let's compute the Fourier expansion of a non-solvable algebraic Maass form.
Here is Magma code that gets you the answer in a few seconds. I made a special case for the bad primes, and did them by hand.
_<x> := PolynomialRing(Rationals());
f5 := 344 + 3106*x - 1795*x^2 - 780* …
- 2,704
11
votes
Accepted
Computing (on a computer) the first few (non-trivial) zeros of the zeta function of a number...
Step I: Put the degree 24 polynomial into Magma, make it a number field, and call LSeries on it. This divides the $L$-function into a product of 7 distinct ones (Dokchitsers code, under an attribute c …
5
votes
Open project: Let's compute the Fourier expansion of a non-solvable algebraic Maass form.
Hmm, a problem. In 4 hours Magma can compute this:
> f:=x^24 - 50726*x^22 + 152929135*x^20 - 158664037068*x^18 + 63787035668165*x^16 -
9040633522810414*x^14 + 287094814384960835*x^12 - 205003861 …
- 2,704
4
votes
Open project: Let's compute the Fourier expansion of a non-solvable algebraic Maass form.
I will copy a comment of mine about Jehanne over here.
His paper is: http://dx.doi.org/10.1006/jnth.2001.2656
Jehanne has 4 totally real Examples 2-5 (page 353-6), including the one of Booker. He al …
- 2,704
3
votes
Open project: Let's compute the Fourier expansion of a non-solvable algebraic Maass form.
Actually, I should read the help with Magma, for the direction to ArtinRepresentations is there.
f:=14488688572801 - 2922378139308818*x^2 + 134981448876235615*x^4 -
1381768039105642956*x^6 + 4 …
- 2,704
3
votes
Open project: Let's compute the Fourier expansion of a non-solvable algebraic Maass form.
I got it to work!
First the preliminary data:
_<x> := PolynomialRing(Rationals());
f5 :=344 + 3106*x - 1795*x^2 - 780*x^3 - x^4 + x^5; …
- 2,704