Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Slavov, Kaloyan"'
Autor:
Slavov, Kaloyan
Let $f_1,\dots,f_m$ be polynomials in $n$ variables with coefficients in a finite field $\mathbb{F}_q$. We estimate the number of points $\underline{x}$ in $\mathbb{F}_q^n$ such that each value $f_i(\underline{x})$ is a nonzero square in $\mathbb{F}_
Externí odkaz:
http://arxiv.org/abs/2407.10538
Autor:
Poonen, Bjorn, Slavov, Kaloyan
Publikováno v:
Bulletin of the London Mathematical Society, 54 (2022), no. 4, 1439-1447
Let $G$ be a subgroup of the symmetric group $S_n$. If the proportion of fixed-point-free elements in $G$ (or a coset) equals the proportion of fixed-point-free elements in $S_n$, then $G=S_n$. The analogue for $A_n$ holds if $n \ge 7$. We give an ap
Externí odkaz:
http://arxiv.org/abs/2107.02724
Autor:
Slavov, Kaloyan
Publikováno v:
Canadian Mathematical Bulletin, 66 (2), 2023, pp. 654-664
We sharpen to nearly optimal the known asymptotic and explicit bounds for the number of $\mathbb{F}_q$-rational points on a geometrically irreducible hypersurface over a (large) finite field. The proof involves a Bertini-type probabilistic combinator
Externí odkaz:
http://arxiv.org/abs/2105.14868
Autor:
Poonen, Bjorn, Slavov, Kaloyan
Publikováno v:
International Mathematics Research Notices, 2020, rnaa182
We introduce a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing over a finite field. Extending a result of Benoist, we prove that for a morphism $\phi \colon X \to \mathbb{P}^n$ such that $
Externí odkaz:
http://arxiv.org/abs/2001.08672
Autor:
Slavov, Kaloyan
Publikováno v:
Acta Arithmetica, 194 (2020), 315-318
Let $f(T)$ be a monic polynomial of degree $d$ with coefficients in a finite field $\mathbb{F}_q$. Extending earlier results in the literature, but now allowing $(q,2d)>1$, we give a criterion for $f$ to satisfy the following property: for all but $d
Externí odkaz:
http://arxiv.org/abs/1903.09050
Autor:
Slavov, Kaloyan
Publikováno v:
Finite Fields and Their Applications, 48 (2017), 60-68
Let $X$ be an absolutely irreducible hypersurface of degree $d$ in $\mathbb{A}^n$, defined over a finite field $\mathbb{F}_q$. The Lang-Weil bound gives an interval that contains $#X(\mathbb{F}_q)$. We exhibit explicit intervals, which do not contain
Externí odkaz:
http://arxiv.org/abs/1703.05062
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 75).
Fix integers n and b with n =/> 3 and 1 =/< b < n - 1. Let k be an a
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 75).
Fix integers n and b with n =/> 3 and 1 =/< b < n - 1. Let k be an a
Externí odkaz:
http://hdl.handle.net/1721.1/64605
Autor:
Slavov, Kaloyan
Publikováno v:
Archiv der Mathematik: Volume 103, Issue 3 (2014), Page 267-277
First, we study constructible subsets of $\A^n_k$ which contain a line in any direction. We classify the smallest such subsets in $\A^3$ of the type $R\cup\{g\neq 0\},$ where $g\in k[x_1,...,x_n]$ is irreducible of degree $d$, and $R\subset V(g)$ is
Externí odkaz:
http://arxiv.org/abs/1410.4328
Autor:
Slavov, Kaloyan
Publikováno v:
Finite Fields and Their Applications, 37 (2016), 158-178
We propose an algebraic geometry framework for the Kakeya problem. We conjecture that for any polynomials $f,g\in\F_{q_0}[x,y]$ and any $\F_q/\F_{q_0}$, the image of the map $\F_q^3\to\F_q^3$ given by $(s,x,y)\mapsto (s,sx+f(x,y),sy+g(x,y))$ has size
Externí odkaz:
http://arxiv.org/abs/1410.3701
Autor:
Slavov, Kaloyan
Publikováno v:
Mathematische Zeitschrift, 279 (2015), no. 1, 139-162
Let $k$ be an algebraically closed field and let $b$ and $n$ be integers with $n\geq 3$ and $1\leq b \leq n-1.$ Consider the moduli space $X$ of hypersurfaces in $\mathbb{P}^n_k$ of fixed degree $l$ whose singular locus is at least $b$-dimensional. W
Externí odkaz:
http://arxiv.org/abs/1208.1118