Questions tagged [number-theory]

Question 1

$LLL$ 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 ...

Question 2

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-...

Question 3

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 ...

Question 4

I am reading an interesting paper One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational by Zudilin. Define $$\varphi_0(x,y):=\sum_{j=1}^{3}([y]+[\eta_0x-y]-[y-\eta_j x]-[(\eta_0-\eta_j)x-y]-2[\...

Question 5

There is a need to increase the number of correct decimal digits from this integral: ...

Question 6

I'm working on an OEIS submission that counts the number of n-digit A157711 primes. Working with PrimeQ as my primality determinator, I can generate some 1200 terms. However, it has been pointed out ...

Question 7

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: ...

Question 8

Given a number, I am trying to find the longest streak of positive divisibility into sequential smaller numbers. Here's an example: We have this 2D list: ...

Question 9

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, ...

Question 10

I am trying to use Mathematica to simplify sums of the form $$\sum_{0 \leq j \leq 5}\sum_{0 \leq k \leq 1}\omega^{nj-k},$$ subject to the polynomial equations $\omega^{6} = 1$ and $\omega^{2} = \omega ...

Question 11

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 ...

Question 12

I was watching this video (2:30 of https://youtu.be/zLEyIT_BCgk?si=ji5NyjR7vcwzaNxi ). Here in the video he said that to get the lattice , we just integrate over the curve(silver line) and we will ...

Question 13

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 ...

Question 14

The list array is: list = Subsets[Range[2, 8], {2}] get the list is: ...

Question 15

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 ...

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Questions tagged [number-theory]

$LLL$ implementation complexity in wolfram mathematica

Find positive-integer tuple satisfying constraints [closed]

DirichletConvolution with an If function returns wrong result

Mathematica code involving floor function

How do you increase the precision and accuracy of the numerical approximation of the Volchkov integral?

Recalcitrant Provable Primes

Complete set of 31 numbers which are not the sum of distinct squares

Count the longest streak output

Having problems with group of units generators

Simplifying Computation Subject to Polynomial Equations

Recognizing Euler products

How to generate lattice by integrating over curves on a modular form domain plot?

Taxicab Geometry

Are there other methods to list the coprime arrays within the array? [duplicate]

Mathematica code to compute a constant

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