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Results tagged with nt.number-theory
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user 56553
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
17
votes
2
answers
2k
views
A set of integers whose factorial can be written as a product of two factorials
I am trying to collect informations concerning the set
$$\mathcal{A}=\left\{n\in\mathbb{N} \mid (\exists k,l\in\{2,3,\dots,n-2\})(n!=k!l!)\right\}.$$
It seems not much is known about the set $\mathcal …
- 2,188
4
votes
0
answers
239
views
A connection between basic hypergeometric series and number theory
I am studying functions given by the power series:
$$f(z)=1+\sum_{n=1}^{\infty}\frac{z^n}{(1-q)(1-q^2)\cdots(1-q^{n})}.$$
The parameter $q$ is usually assumed to be such that $|q|<1$. Then it is easy …
- 2,188
3
votes
Equation about Jacobi Theta Functions
By using standard identities from the theory of Elliptic functions, you can prove it at least for the real nome $q\in(-1,1)$. There are actually many identities involving products of Theta functions. …
- 2,188