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English is not my native tongue. German is not my native tongue. French is not my native tongue.


1d
comment how to calculate the sum of remainders of N?
Please use TeX properly on this site. Also, it is not clear what you mean by "reminder" as there are different conventions around (e.g. the residue of 7 modulo 4 equals -1).
1d
comment Parabolic subgroup
Please use TeX on this site.
1d
comment Weyl group representation
Please use TeX on this site.
Jan
26
comment Parametric solutions of Pell's equation
Well, saying that "$n=13$ belong to two series" suggests that you fix $n$ and look for parametric solutions of $a^2-nb^2=1$ in the remaining variables $a$ and $b$. Perhaps saying that the "initial value $n=13$ belongs to two series" would be more appropriate. This just a language thing, of course, because your question is clear about what you are after.
Jan
26
comment Parametric solutions of Pell's equation
I think it is misleading to say that $n=13$ belongs to two series. Changing the parameter $k$ in your example changes all three variables in the Pell equation $a^2-nb^2=1$, including $n$.
Jan
25
revised References for general Hasse-Weil zeta function
edited tags
Jan
25
revised Shortest/Most elegant proof for $L(1,\chi)\neq 0$
edited tags
Jan
24
comment Rankin-Selberg convolution and product of degrees
@paulgarrett: You should turn your comment into answer, so that this question can be closed. Perhaps you can mention the pairs $(n,n')$ when we know the statement.
Jan
23
revised Can a graph be reconstructed from its cycle lengths?
edited tags
Jan
23
revised Finding the greatest (smallest) factor of a number smaller (greater) than another number
edited tags; edited title
Jan
22
comment Has this formula about prime gaps already been conjectured and/or proven?
@YaakovBaruch: It is common to use this notation where higher iterates of log frequently occur, e.g. in certain branches of number theory and combinatorics. For example, Maynard's paper (arxiv.org/abs/1408.5110) uses this notation.
Jan
22
comment Has this formula about prime gaps already been conjectured and/or proven?
@TerryTao: You beat me by a few seconds, and of course your answer is better because it builds on earlier results.
Jan
22
answered Has this formula about prime gaps already been conjectured and/or proven?
Jan
22
revised Fixed field of the Nebentypus of a newform for $\Gamma_1(N)$
edited tags
Jan
20
comment Is $ a^2b^2-ab-ap$ a perfect square for suitable $a,b\in \mathbb{Z}^+$?
@KasperAndersen: Thank you! I am somewhat surprised, but I admit I have little experience with the Erdős-Straus conjecture.
Jan
20
comment Mean value of Maass forms
For clarity I would add after your last sentence the following. "This way one can see that for any $\epsilon>0$ we have $\limsup_{j\to\infty}|\langle\phi_j,\chi_A\rangle|\leq\epsilon$, whence $\lim_{j\to\infty}\langle\phi_j,\chi_A\rangle=0$."
Jan
20
comment Is $ a^2b^2-ab-ap$ a perfect square for suitable $a,b\in \mathbb{Z}^+$?
@TerryTao: Very interesting, thank you!
Jan
20
revised Is $ a^2b^2-ab-ap$ a perfect square for suitable $a,b\in \mathbb{Z}^+$?
deleted 2 characters in body; edited title
Jan
19
revised Is $ a^2b^2-ab-ap$ a perfect square for suitable $a,b\in \mathbb{Z}^+$?
deleted 11 characters in body
Jan
19
comment Is $ a^2b^2-ab-ap$ a perfect square for suitable $a,b\in \mathbb{Z}^+$?
After some thinking, I arrived at the following equivalent condition: there are positive integers $\ell$ and $m$ such that $m\mid\ell^2$ and $p+m\equiv 0\pmod{4\ell-1}$. I think it is possible that a counterexample exists, but justifying it might be very difficult. By the way, your title is misleading as being squareful is different from being a square.