Zobrazeno 1 - 10
of 31
pro vyhledávání: '"68R05, 11B75"'
Autor:
Rudnev, Misha
A regular linear line complex is a three-parameter set of lines in space, whose Pl\"ucker vectors lie in a hyperplane, which is not tangent to the Klein quadric. Our main result is a bound $O(n^{1/2}m^{3/4} + m+n)$ for the number of incidences betwee
Externí odkaz:
http://arxiv.org/abs/2003.04744
Autor:
Rudnev, Misha
It is shown that the number of distinct types of three-point hinges, defined by a real plane set of $n$ points is $\gg n^2\log^{-3} n$, where a hinge is identified by fixing two pair-wise distances in a point triple. This is achieved via strengthenin
Externí odkaz:
http://arxiv.org/abs/1902.05791
Let $F$ be a field and a finite $A\subset F$ be sufficiently small in terms of the characteristic $p$ of $F$ if $p>0$. We strengthen the "threshold" sum-product inequality $$|AA|^3 |A\pm A|^2 \gg |A|^6\,,\;\;\;\;\mbox{hence} \;\; \;\;|AA|+|A+A|\gg |A
Externí odkaz:
http://arxiv.org/abs/1808.08465
We prove new results on additive properties of finite sets $A$ with small multiplicative doubling $|AA|\leq M|A|$ in the category of real/complex sets as well as multiplicative subgroups in the prime residue field. The improvements are based on new c
Externí odkaz:
http://arxiv.org/abs/1712.00410
Autor:
Rudnev, Misha
It is shown that for a finite set $A$ of four or more complex numbers, the cardinality of the set $C[A]$ of all cross-ratios generated by quadruples of pair-wise distinct elements of $A$ is $|C[A]|\gg |A|^{2+\frac{2}{11}}\log^{-\frac{6}{11}} |A|$ and
Externí odkaz:
http://arxiv.org/abs/1705.01830
We prove new exponents for the energy version of the Erd\H{o}s-Szemer\'edi sum-product conjecture, raised by Balog and Wooley. They match the previously established milestone values for the standard formulation of the question, both for general field
Externí odkaz:
http://arxiv.org/abs/1607.05053
This paper is an erratum to our paper, entitled "On an application of Guth-Katz theorem", Math. Res. Lett. 18 (2011), no. 4, 691-697. Let $F$ be the real or complex field and $\omega$ a non-degenerate skew-symmetric bilinear form in the plane $F^2$.
Externí odkaz:
http://arxiv.org/abs/1512.02670
Autor:
Rudnev, Misha
We prove that a finite subset $A$ of the projective line $FP^1$ over a field $F$ of positive characteristic $p$ determines $\Omega(|A|^2)$ distinct cross-ratios, as long as $|A|<\sqrt{p}.$
Comment: This article had been earlier withdrawn by the
Comment: This article had been earlier withdrawn by the
Externí odkaz:
http://arxiv.org/abs/1508.05142
Autor:
Rudnev, Misha, Selig, J. M.
Publikováno v:
SIAM J. Discrete Math. 30-2 (2016), pp. 934-954 (does not contain the latter addition)
We discuss a unified approach to a class of geometric combinatorics incidence problems in $2D$, of the Erd\"os distance type. The goal is obtaining the second moment estimate, that is given a finite point set $S$ and a function $f$ on $S\times S$, an
Externí odkaz:
http://arxiv.org/abs/1412.2909
Publikováno v:
Adv. Math. 293 (2016) 589-605
Let $F$ be a field with positive odd characteristic $p$. We prove a variety of new sum-product type estimates over $F$. They are derived from the theorem that the number of incidences between $m$ points and $n$ planes in the projective three-space $P
Externí odkaz:
http://arxiv.org/abs/1408.0542