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1d
revised Which theta function is $\theta(x;q) = (x;q)(q/x;q)$?
added 157 characters in body
1d
asked Which theta function is $\theta(x;q) = (x;q)(q/x;q)$?
2d
revised A simple way to find $\lim_{n\rightarrow\infty}{\frac{1}{n^2}\sum_{k=1}^n{\sqrt{n^2-k^2}}}$
added 13 characters in body
2d
revised A simple way to find $\lim_{n\rightarrow\infty}{\frac{1}{n^2}\sum_{k=1}^n{\sqrt{n^2-k^2}}}$
added 375 characters in body
2d
answered A simple way to find $\lim_{n\rightarrow\infty}{\frac{1}{n^2}\sum_{k=1}^n{\sqrt{n^2-k^2}}}$
2d
revised How does one prove that $\mathbb{Z}\left[\frac{1 + \sqrt{-43}}{2}\right]$ is a unique factorization domain.
edited title
2d
comment Visual proof of $\sum_{n=1}^\infty \frac{1}{n^4} = \frac{\pi^4}{90}$?
the only visualization I can think of is in 4 dimensions, finishing Robert Israel's proof. Is that okay? I could try to project the darn thing myself.
May
27
revised How does one prove that $\mathbb{Z}\left[\frac{1 + \sqrt{-43}}{2}\right]$ is a unique factorization domain.
added 181 characters in body
May
27
comment How does one prove that $\mathbb{Z}\left[\frac{1 + \sqrt{-43}}{2}\right]$ is a unique factorization domain.
@AlonsodelArte Do you mean $\mathbb{Z}[\frac{1 + \sqrt{-41}}{2}]$ or $\mathbb{Z}[\sqrt{-41}]$ ? I meant $\sqrt{-43}$.
May
27
asked How does one prove that $\mathbb{Z}\left[\frac{1 + \sqrt{-43}}{2}\right]$ is a unique factorization domain.
May
27
comment Can we find the 18 imaginary quadratic ffields with class number 2 algorithmically?
@BillDubuque it is indeed; don't be surprised if I revise this question or post another one asking for more details
May
26
revised Can we find the 18 imaginary quadratic ffields with class number 2 algorithmically?
added 356 characters in body; edited title
May
26
revised Can we find the 18 imaginary quadratic ffields with class number 2 algorithmically?
added 356 characters in body; edited title
May
26
asked Can we find the 18 imaginary quadratic ffields with class number 2 algorithmically?
May
24
comment Certain local inequality for volume and surface measures
Locally isnt a smooth curve just a line segment? Since you are integrating near $x$?
May
24
revised Without using Heegner-Stark-Baker, $\mathbb{Q}(\sqrt{-11})$ has class number $1$.
Introductory text
May
23
comment Prove: $\gcd(n^a-1,n^b-1)=n^{\gcd(a,b)}-1$
You raise an interesting point. My argument is simple but unfortunatetly does not prove the result. I will ask a question on this site
May
23
comment Prove: $\gcd(n^a-1,n^b-1)=n^{\gcd(a,b)}-1$
I am not asking you for permission here. Then use cyclotomic polynomials if you are dissatisfied. I think we have shown that $\mathbb{Q}[x]/(x^a-1,x^b-1)$ is a very interesting ring.
May
23
comment Prove: $\gcd(n^a-1,n^b-1)=n^{\gcd(a,b)}-1$
Uh... If I hate zero divisors I can remove factors of $(x-1)$ and extend by $1+x+...+x^{a-1}$. And multiply it back each time. That way only adjoin primitive roots of unity.
May
23
comment Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
Sort of like the Fibonacci sequence!