DmitryZ
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 May 14 revised Low height integer points on a rank variety added 62 characters in body May 14 comment Low height integer points on a rank variety Yes, and it may also depend on the size of the matrices. May 13 asked Low height integer points on a rank variety Sep 24 awarded Autobiographer Aug 23 awarded Yearling Aug 17 awarded Nice Question Jul 2 awarded Curious May 5 asked Cassels-Birch-Davenport theorem for multiple quadratic forms of certain type Apr 22 revised Maximal $k$-chordal subgraph the answer for the last question is NO Apr 22 asked Maximal $k$-chordal subgraph Apr 9 comment Find minimal set of progressions which intersections, unions or negations covers given set What if you take a set with no 3-term APs? There are known examples when such a set is fairly big. Apr 9 comment Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$ Thanks a lot. So I accept your answer as now I can safely say that without GRH the problem is hard and wide open. Apr 9 accepted Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$ Apr 9 comment Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$ Correct me if I am wrong but it seems that the unconditional version of the Chebotaryov density is just not strong enough to provide the desired bound (and the conditional version does give it), since the power beta goes to 1 as N is large. Apr 9 asked Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$ Feb 10 comment Number of solutions of linear homogenous Diophantine equation inside a box Thanks for the nice answer. In fact, it works for all boxes larger than some constant which depend only on $d$ and $c$, which is important since in my case $a_i$ may depend on $N$ but not on the dimension and $c$. Feb 10 accepted Number of solutions of linear homogenous Diophantine equation inside a box Feb 10 comment Number of solutions of linear homogenous Diophantine equation inside a box What do you mean by averaging? since the equation is homogeneous one can of course assume that $a_i$ sum up to $1$. Feb 8 comment Number of solutions of linear homogenous Diophantine equation inside a box Thanks, but after a quick look it seems that they always assume the coefficients are at least rational, don't they? Feb 7 asked Number of solutions of linear homogenous Diophantine equation inside a box