Results 11 to 20 of about 299 (26)
Value sets of sparse polynomials [PDF]
, 2018 We obtain a new lower bound on the size of value set f(F_p) of a sparse polynomial f in F_p[X] over a finite field of p elements when p is prime. This bound is uniform with respect of the degree and depends on some natural arithmetic properties of the ...
Shparlinski, Igor E. +1 more
core +2 more sources
The probability that a complete intersection is smooth [PDF]
, 2012 Given a smooth subscheme of a projective space over a finite field, we compute the probability that its intersection with a fixed number of hypersurface sections of large degree is smooth of the expected dimension.
Bucur, Alina, Kedlaya, Kiran S.
core +2 more sources
Curves, dynamical systems and weighted point counting [PDF]
, 2012 Suppose X is a (smooth projective irreducible algebraic) curve over a finite field k. Counting the number of points on X over all finite field extensions of k will not determine the curve uniquely. Actually, a famous theorem of Tate implies that two such
Cornelissen, Gunther
core +1 more source
On the nonexistence of certain curves of genus two [PDF]
, 2002 We prove that if q is a power of an odd prime then there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (2-2q)x^2 + q^2.
Howe, Everett W.
core +2 more sources
Toward a geometric analogue of Dirichlet's unit theorem [PDF]
, 2014 In this note, we propose a geometric analogue of Dirichlet's unit theorem on arithmetic varieties, that is, if X is a normal projective variety over a finite field and D is a pseudo-effective Q-Cartier divisor on X, does it follow that D is Q-effective ...
Moriwaki, Atsushi
core +3 more sources
Automorphisms of Drinfeld half-spaces over a finite field [PDF]
, 2012 We show that the automorphism group of Drinfeld's half-space over a finite field is the projective linear group of the underlying vector space. The proof of this result uses analytic geometry in the sense of Berkovich over the finite field equipped with ...
Amaury Thuillier +6 more
core +3 more sources
Rational points on certain hyperelliptic curves over finite fields
, 2007 Let $K$ be a field, $a, b\in K$ and $ab\neq 0$. Let us consider the polynomials $g_{1}(x)=x^n+ax+b, g_{2}(x)=x^n+ax^2+bx$, where $n$ is a fixed positive integer.
Ulas, Maciej
core +1 more source
Lattices with exponentially large kissing numbers
, 2018 We construct a sequence of lattices $\{L_{n_i}\subset \mathbb R^{n_i}\}$ for $n_i\longrightarrow\infty$, with exponentially large kissing numbers, namely, $\log_2\tau(L_{n_i})> 0.0338\cdot n_i -o(n_i)$.
Vlăduţ, Serge
core +1 more source
Factorization type probabilities of polynomials with prescribed coefficients over a finite field
, 2020 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^2-d-
Slavov, Kaloyan
core
The structure of Deitmar Schemes, II. Zeta functions and automorphism groups [PDF]
, 2016 We provide a coherent overview of a number of recent results obtained by the authors in the theory of schemes defined over the field with one element.
Merida-Angulo, Manuel, Thas, Koen
core +1 more source