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Terne di quadrati consecutivi in un campo di Galois

Umberto Bartocci, Emanuela Ughi (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Explicit formulae for the number of triplets of consecutive squares in a Galois field F q are given.

The Divisibility Modulo 4 of Kloosterman Sums over Finite Fields of Characteristic 3

Sin, Changhyon (2011)

Serdica Journal of Computing

Recently Garashuk and Lisonek evaluated Kloosterman sums K (a) modulo 4 over a finite field F3m in the case of even K (a). They posed it as an open problem to characterize elements a in F3m for which K (a) ≡ 1 (mod4) and K (a) ≡ 3 (mod4). In this paper, we will give an answer to this problem. The result allows us to count the number of elements a in F3m belonging to each of these two classes.

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

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 [6, 3, 4] and using a slightly different method, we study the fluctuations in the number of 𝔽 q -points on the curve F given by the affine model 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 irreducible...

The fundamental theorem of prehomogeneous vector spaces modulo p m (With an appendix by F. Sato)

Raf Cluckers, Adriaan Herremans (2007)

Bulletin de la Société Mathématique de France

For a number field K with ring of integers 𝒪 K , we prove an analogue over finite rings of the form 𝒪 K / 𝒫 m of the fundamental theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where 𝒫 is a big enough prime ideal of 𝒪 K and m > 1 . In the appendix, F.Sato gives an application of the Theorems 1.1, 1.3 and the Theorems A, B, C in J.Denef and A.Gyoja [Character sums associated to prehomogeneous vector spaces, Compos. Math., 113(1998), 237–346] to the functional equation of L -functions...

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