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Results tagged with nt.number-theory
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user 100873
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
0
votes
0
answers
149
views
Mertens' Third Theorem for primes of the form $4n+1$
I am looking for upper and lower bounds for the following expression:
$$\prod_{\substack{p\le n \\ p \equiv 1\ mod\ 4}} \frac{p-1}{p}$$
Apart from the trivial one:
$$\prod_{\substack{p\le n \\ p \equi …
- 6,367
3
votes
1
answer
746
views
Gauss' Circle Problem at $\left ( \frac{1}{2}, \frac{1}{2} \right ) $
GCP (Gauss' Circle Problem) asks for a closed form for the number of square-lattice points inside a circle, centered at the origin, of radius $r$.
Let's denote by $N(r)$ the number of these points. T …
- 193
1
vote
1
answer
531
views
Proof claimed of Gauss' Circle Problem
I just wanted to ask wether this problem has already been proved or not.
I know that there are 2 other posts that deal with exactly the same question, but I decided to ask it again, since they are t …
- 105k