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Jan
24
revised Character values bounded away from zero
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Jan
24
comment Character values bounded away from zero
@M.Shahryari: I mean of course that there are values $k$ (e.g. when $k$ is about $n/4$) where the value is close to $\cos(\pi/2)=0$.
Jan
23
answered Character values bounded away from zero
Jan
23
comment Character values bounded away from zero
I think the two dimensional representations of the dihedral groups will already give such an example.
Jan
23
comment How many integer points does my favorite ellipse goes through?
Just multiply by one more prime that is $1\pmod 3$; for example $61$.
Jan
21
comment On the number N(x,y) of those integers n<x, with squarefree core k(n)<y
Perron's formula in $s$ gives you the terms with $n\le x$, and Perron's formula in $t$ gives you the terms with $k(n)\le y$. Hence the RHS equals $N(x,y)$. Also you might mention that you are trying to read the nice recent work of Robert and Tenenbaum: dossier.univ-st-etienne.fr/rool6510/www/index.html .
Jan
18
revised summation of products of combinatorials
added 121 characters in body
Jan
18
revised summation of products of combinatorials
The original question was unclear (see comments below). Edited to clarify this.
Jan
18
answered summation of products of combinatorials
Jan
17
comment Elementary proof of bounds on factor polynomials
Why do you spell it as Gelfand rather than Gelfond? At least according to wikipedia, the name of Alexander Gelfond is spelt with an o, and Israel Gelfand with an a; not only in English, but also in Russian.
Jan
17
reviewed Looks OK References for well-posedness of weak solutions to Stefan problem
Jan
17
reviewed Close Is discrete mathematics mainstream?
Jan
16
reviewed Approve A Poincaré-type inequality with logarithmic function
Jan
16
comment Consecutive Primes mod 3
@bobuhito: No I don't think we can (provably) rule out the probabilities that you mention.
Jan
16
comment Consecutive Primes mod 3
Shiu's result is an unconditional theorem. The preprint of Banks et al linked above gives the reference (and also a different proof of Shiu's result based on Maynard's recent work).
Jan
16
comment Consecutive Primes mod 3
One more comment: Work of Daniel Shiu shows that arbitrarily long strings of consecutive $1$'s (or consecutive $2$'s) will appear in this sequence. In particular this rules out the $12$ cycling forever. See also the recent preprint of Banks et al: arxiv.org/pdf/1311.7003v2.pdf .
Jan
16
comment Consecutive Primes mod 3
See the discussion in the comments of mathoverflow.net/questions/153656/… . It addresses essentially questions of your flavor. Not too much is probably known about the complexity of this sequence, but recent progress on primes would say something as Terry Tao indicates in these comments.
Jan
16
comment summation of products of combinatorials
The problem is not completely clear to me. Is $\sigma$ really a tuple, or a set? If it is an ordered tuple then the formula for $C_N^n$ seems off. If you really want to sum over sets, the limit seems to be zero: the product is at most $N!/(N-n)!$, and the number of sets is at most $2^N$ so the desired quantity is at most $2^N/(N-n)!$.
Jan
15
comment The simple zero conjecture for the Riemann zeta function
For a zero with imaginary part around $T$, we don't know anything beyond the fact that the multiplicity is bounded by a constant times $\log T$. Even RH would only allow the slightly better result that the multiplicity is bounded by a constant $\log T/\log \log T$. The analogous problem for the multiplicity of a zero at $1/2$ for the $L$-function of an elliptic curve has been extensively studied (e.g. by Brumer).
Jan
15
reviewed Approve The “Level N modular equation for delta” in characteristics 3, 5, 7 and 13