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English is not my native tongue.


19h
comment Does the Gamma function preserve integers?
@VítTuček: Thank you, that makes sense.
Oct
18
revised Fermat's little theorem with smaller powers
edited tags
Oct
16
comment Does the Gamma function preserve integers?
I think the same argument works with the simpler expression $\Gamma(z)\Gamma(1-z)$.
Oct
15
revised Why do $12$ and $120$ occur very often in the denominators of $\zeta(-n)$ for odd $n$?
added 1 character in body
Oct
15
revised Why do $12$ and $120$ occur very often in the denominators of $\zeta(-n)$ for odd $n$?
edited tags
Oct
15
revised Why do $12$ and $120$ occur very often in the denominators of $\zeta(-n)$ for odd $n$?
added 231 characters in body
Oct
15
answered Why do $12$ and $120$ occur very often in the denominators of $\zeta(-n)$ for odd $n$?
Oct
9
answered Asking for an English version of a paper
Sep
30
awarded  Explainer
Sep
25
revised “Must read ”papers on analytic number theory
edited tags
Sep
24
awarded  Autobiographer
Sep
23
comment is $x_{n}\ll \overline{x}_{n}^{2}$?
@SylvainJULIEN: My example satisfies the stronger bound $x_n\leq n$ which clearly implies $\overline{x}_{n}<n/2$.
Sep
23
revised is $x_{n}\ll \overline{x}_{n}^{2}$?
added 25 characters in body
Sep
23
answered is $x_{n}\ll \overline{x}_{n}^{2}$?
Sep
22
comment The angular distribution of the $(a,b)$ in $p = a^2+b^2$, and the distribution of the lattices corresponding to prime ideals
Sorry, I had a typo, I meant $L(1,\chi)\neq 0$. And yes, I meant equidistribution with respect to the uniform measure.
Sep
22
awarded  Nice Answer
Sep
22
comment The angular distribution of the $(a,b)$ in $p = a^2+b^2$, and the distribution of the lattices corresponding to prime ideals
I have to run now, but $L(1,\chi)\neq 1$ for unramified Hecke characters $\chi$ of $\mathbb{Q}(i)$ implies that $(a,b)$ is equidistributed in angle (in the sense that if you take a large disc etc.)
Sep
21
comment Solution or Reference Request for a Closed Form of the Sum
Do not expect any simple expression for the Legendre function. It is a complicated function in the sense that we cannot answer (even approximately) simple questions like: for a given $q$, how small is the smallest $a\geq 1$ with $\left(\frac{a}{q}\right)=-1$ (cf. en.wikipedia.org/wiki/…). We like quadratic reciprocity (among other things) because it allows us to calculate the Legendre symbol in polynomial time.
Sep
21
comment Solution or Reference Request for a Closed Form of the Sum
@user170039: See my comment to your original post.
Sep
20
answered Solution or Reference Request for a Closed Form of the Sum