Questions tagged [number-theory]
Questions on the number-theoretic functionality of Mathematica.
465 questions
1 vote
1 answer
143 views
$LLL$ implementation complexity in wolfram mathematica
$LLL$ is implemented in Wolfram Mathematica as $\mathsf{LatticeReduce}$ command. If we want to reduce a rank $k\leq n$ lattice in $\mathbb Z^n$ where the generator matrix of the lattice has integral ...
- 157
0 votes
1 answer
92 views
DirichletConvolution with an If function returns wrong result
I want to compute a Dirichlet convolution with a function that has a conditional. For simplicity, let's say: idifeven[n_]:=If[EvenQ[n],n,0] Let's convolve this ...
- 21
6 votes
1 answer
672 views
How do you increase the precision and accuracy of the numerical approximation of the Volchkov integral?
There is a need to increase the number of correct decimal digits from this integral: ...
- 1,221
7 votes
1 answer
476 views
Complete set of 31 numbers which are not the sum of distinct squares
A001422 gives the whole set of 31 numbers which are not the sum of distinct squares (see also MathWorld). That article also provides code for it: ...
- 74.9k
10 votes
2 answers
400 views
Having problems with group of units generators
Sorry if the question is quite basic, I started learning Mathematica today to help me with group computations. I'm trying to get the generators of the group of units modulo p, with p a prime. However, ...
- 103
11 votes
5 answers
660 views
Recognizing Euler products
Is there a standard approach in Mathematica for recognizing Euler products? For example, I have the following product $$\prod_{p} \frac{1-p^{s}+p^{2s}}{\left(p^s-1\right)^2}.$$ There is a nice closed ...
- 213
9 votes
3 answers
1k views
Taxicab Geometry
According to taxicab geometry, there are 1226 possible paths from A(2,5) to B(7,9), all with a distance of 9 units, |2-7|+|9-5|=9. I wanted to write a code where I could be obtaining the plots of some ...
1 vote
1 answer
232 views
Mathematica code to compute a constant
I am reading an interesting paper One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational by Zudilin. We fix odd numbers $q$ and $r$, $q\geq r+4$ and a tuple $\eta_0,\eta_1,...,\eta_q$ of positive ...
- 373