Displaying similar documents to “Standard monomials for q-uniform families and a conjecture of Babai and Frankl”

Computations with Witt vectors of length 3

Luís R. A. Finotti (2011)

Journal de Théorie des Nombres de Bordeaux

Similarity:

In this paper we describe how to perform computations with Witt vectors of length 3 in an efficient way and give a formula that allows us to compute the third coordinate of the Greenberg transform of a polynomial directly. We apply these results to obtain information on the third coordinate of the j -invariant of the canonical lifting as a function on the j -invariant of the ordinary elliptic curve in characteristic p .

The fluctuations in the number of points on a family of curves over a finite field

Maosheng Xiong (2010)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let l ≥ 2 be a positive integer, 𝔽 q a finite field of cardinality q with q ≡ 1 ( mod l ) . In this paper, inspired by [, , ] and using a slightly different method, we study the fluctuations in the number of 𝔽 q -points on the curve ℂ F given by the affine model ℂ F : Y l = F ( X ) , where F is drawn at random uniformly from the set of all monic l -th power-free polynomials F ∈ 𝔽 q [ X ] of degree d as d → ∞ . The method also enables us to study the fluctuations in the number of 𝔽 q -points on the same family of curves arising from the set of monic...

On the Carlitz problem on the number of solutions to some special equations over finite fields

Ioulia N. Baoulina (2011)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We consider an equation of the type a 1 x 1 2 + ⋯ + a n x n 2 = b x 1 ⋯ x n over the finite field 𝔽 q = 𝔽 p s . Carlitz obtained formulas for the number of solutions to this equation when n = 3 and when n = 4 and q ≡ 3 ( mod 4 ) . In our earlier papers, we found formulas for the number of solutions when d = gcd ( n - 2 , ( q - 1 ) / 2 ) = 1 or 2 or 4 ; and when d > 1 and - 1 is a power of p modulo  2 d . In this paper, we obtain formulas for the number of solutions when d = 2 t , t ≥ 3 , p ≡ 3 or 5 ( mod 8 ) or p ≡ 9 ( mod 16 ) . For general case, we derive lower bounds for the number of solutions.

On the K-theory of tubular algebras

Dirk Kussin (2000)

Colloquium Mathematicae

Similarity:

Let Λ be a tubular algebra over an arbitrary base field. We study the Grothendieck group K 0 ( Λ ) , endowed with the Euler form, and its automorphism group A u t ( K 0 ( Λ ) ) on a purely K-theoretical level as in [7]. Our results serve as tools for classifying the separating tubular families of tubular algebras as in the example [5] and for determining the automorphism group A u t ( D b Λ ) of the derived category of Λ.

A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm

Jun-ichi Tamura (1992)

Acta Arithmetica

Similarity:

In this paper, we give transcendental numbers φ and ψ such that (i) both φ and ψ have explicit g-adic expansions, and simultaneously, (ii) the vector t ( φ , ψ ) has an explicit expression in the Jacobi-Perron algorithm (cf. Theorem 1). Our results can be regarded as a higher-dimensional version of some of the results in [1]-[5] (see also [6]-[8], [10], [11]). The numbers φ and ψ have some connection with algebraic numbers with minimal polynomials x³ - kx² - lx - 1 satisfying (1.1) k ≥ l ≥0, k...