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Results tagged with analytic-number-theory
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user 121
On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.
5
votes
Reference for a conjecture on the first primes congruent to 1 modulo other primes
For your parenthetical request: S. Chowla, On the least prime in an arithmetic progression. J. Indian Math. Soc. 1 (1934) 1-3.
- 45.7k
10
votes
Accepted
What is the Stirling formula for x(x+1)(x+2)...(x+n-1)?
It looks like you want a formula for the asymptotics of the Pochhammer symbol $(x)_n$ as $n \to \infty$. One such formula is provided about halfway down Wolfram's page:
$$(x)_n \sim \frac{\sqrt{2\pi} …
- 45.7k
35
votes
Why Is $e^{\pi\sqrt{232}}$ an Almost Integer?
The standard reason why $e^{\pi\sqrt{N}}$ is a near integer for some $N$ is that there is some modular function $f$ with $q$-expansion $q^{-1} + O(q)$, such that substituting $\tau = \frac{1 + i\sqrt …
- 45.7k
7
votes
Accepted
Analogues of the Monster for central charges different from 24
As others have mentioned, there are many CFTs, but we can narrow down our list by looking at conditions that select for interesting automorphism groups. Perhaps the easiest is to consider holomorphic …
- 45.7k
12
votes
Accepted
There is no lattice in PSL(2,R) which contains PSL(2,Z) properly?
We can say something stronger.
Theorem: (Helling 1976) Consider the family of subgroups of $SL_2(\mathbb{C})$ that are commensurable with a conjugate of $SL_2(\mathbb{Z})$. The maximal elements o …
- 45.7k
3
votes
Prime numbers $p$ not of the form $ab + bc + ac$ $(0 < a < b < c )$ (and related questions)
Partial answer: Set a=1, so you want to enumerate the primes of the form b+c+bc = (b+1)(c+1)-1. This covers all primes p such that p+1 is a product of two factors of size at least 3. The leftovers ( …
- 45.7k