共查询到20条相似文献,搜索用时 31 毫秒
1.
Generalizing the norm and trace mappings for
qr/
q, we introduce an interesting class of polynomials over finite fields and study their properties. These polynomials are then used to construct curves over finite fields with many rational points. 相似文献
2.
Robert S. Coulter 《Finite Fields and Their Applications》2002,8(4):397
We determine the number of
q-rational points of a class of Artin–Schreier curves by using recent results concerning evaluations of some exponential sums. In particular, we determine infinitely many new examples of maximal and minimal plane curves in the context of the Hasse–Weil bound. 相似文献
3.
Michael J. Johnson 《Journal of Approximation Theory》2000,107(2):163
The problem of approximating smooth Lp-functions from spaces spanned by the integer translates of a radially symmetric function φ is very well understood. In case the points of translation, Ξ, are scattered throughout
d, the approximation problem is only well understood in the “stationary” setting. In this work, we provide lower bounds on the obtainable approximation orders in the “non-stationary” setting under the assumption that Ξ is a small perturbation of
d. The functions which we can approximate belong to certain Besov spaces. Our results, which are similar in many respects to the known results for the case Ξ=
d, apply specifically to the examples of the Gauss kernel and the generalized multiquadric. 相似文献
4.
Florian Breuer 《Transactions of the American Mathematical Society》2007,359(3):1351-1374
Let be a product of Drinfeld modular curves over a general base ring of odd characteristic. We classify those subvarieties of which contain a Zariski-dense subset of CM points. This is an analogue of the André-Oort conjecture. As an application, we construct non-trivial families of higher Heegner points on modular elliptic curves over global function fields.
5.
Larry Smith 《Finite Fields and Their Applications》2002,8(4):504
Let
q be the finite field with q elements, q=pν, p
a prime, and Mat2.2(
q) the vector space of 2×2-matrices over
. The group GL(2,
) acts on Mat2,2(
q) by conjugation. In this note, we determine the invariants of this action. In contrast to the case of an infinite field, where the trace and determinant generate the ring of invariants, several new invariants appear in the case of finite fields. 相似文献
6.
Stphane Ballet 《Finite Fields and Their Applications》2003,9(4):472
From the existence of a tower of algebraic function fields with more steps than the Garcia–Stichtenoth tower, we improve upper bounds on the bilinear complexity of multiplication in all extensions of the finite field
where q is an arbitrary prime power. 相似文献
7.
Nicholas Hanges 《Journal of Functional Analysis》2004,210(2):295-320
We study a partial differential operator
with analytic coefficients, which is of the form “sum of squares”.
is hypoelliptic on any open subset of
, yet possesses the following properties: (1)
is not analytic hypoelliptic on any open subset of
that contains 0. (2) If u is any distribution defined near
with the property that
is analytic near 0, then u must be analytic near 0. (3) The point 0 lies on the projection of an infinite number of Treves curves (bicharacteristics).These results are consistent with the Treves conjectures. However, it follows that the analog of Treves conjecture, in the sense of germs, is false.As far as we know,
is the first example of a “sum of squares” operator which is not analytic hypoelliptic in the usual sense, yet is analytic hypoelliptic in the sense of germs. 相似文献
8.
Richard F. Bass Krzysztof Burdzy 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2001,37(6):627
For
, we consider Lft, the local time of space-time Brownian motion on the curve f. Let
be the class of all functions whose Hölder norm of order α is less than or equal to 1. We show that the supremum of Lf1 over f in
is finite if α>1/2 and infinite if α<1/2. 相似文献
9.
Paulo H. Viana Jaime E. A. Rodriguez 《Bulletin of the Brazilian Mathematical Society》2005,36(1):39-58
A curve defined over a finite field is maximal or minimal according to whether the number of rational points attains the upper or the lower bound in Hasse-Weils theorem, respectively. In the study of maximal curves a fundamental role is played by an invariant linear system introduced by Rück and Stichtenoth in [6]. In this paper we define an analogous invariant system for minimal curves, and we compute its orders and its Weierstrass points. In the last section we treat the case of curves having genus three in characteristic two. 相似文献
10.
Maxim Nazarov 《European Journal of Combinatorics》2004,25(8):1345-1376
Let
be the affine Hecke algebra corresponding to the group GLl over a p-adic field with residue field of cardinality q. We will regard
as an associative algebra over the field
. Consider the
-module W induced from the tensor product of the evaluation modules over the algebras
and
. The module W depends on two partitions λ of l and μ of m, and on two non-zero elements of the field
. There is a canonical operator J acting on W; it corresponds to the trigonometric R-matrix. The algebra
contains the finite dimensional Hecke algebra Hl+m as a subalgebra, and the operator J commutes with the action of this subalgebra on W. Under this action, W decomposes into irreducible subspaces according to the Littlewood–Richardson rule. We compute the eigenvalues of J, corresponding to certain multiplicity-free irreducible components of W. In particular, we give a formula for the ratio of two eigenvalues of J, corresponding to the “highest” and the “lowest” components. As an application, we derive the well known q-analogue of the hook-length formula for the number of standard tableaux of shape λ. 相似文献
11.
G. Min 《Journal of Approximation Theory》1999,98(2):197
This note characterizes the denseness of rational systems
in C[−1, 1], where the nonreal poles in {ak}∞k=1
\[−1, 1] are paired by complex conjugation. This extends an Achiezer's result. 相似文献
Full-size image
12.
Let f(x) be a strongly primitive polynomial of degree n over Z/(2e), η(x0,x1,…,xe−2) a Boolean function of e−1 variables and (x0,x1,…,xe−1)=xe−1+η(x0,x1,…,xe−2)G (f(x),Z/(2e)) denotes the set of all sequences over Z/(2e) generated by f(x), F2∞ the set of all sequences over the binary field F2, then the compressing mapping
is injective, that is, for
,
G(f(x),Z/(2e)),
=
if and only if Φ(
)=Φ(
), i.e., (
0,…,
e−1)=(
0,…,
e−1) mod 2. In the second part of the paper, we generalize the above result over the Galois rings. 相似文献
Full-size image
13.
So Young Choi 《Journal of Number Theory》2006,119(1):18-27
In this work, we find plane models for certain Drinfeld modular curves X0(n) which have better properties than the plane models derived from the usual Drinfeld modular equations. As an application, we construct ring class fields over imaginary quadratic fields by using singular values of generators of the function field of X0(n). 相似文献
14.
The flag geometry Γ=(
,
, I) of a finite projective plane Π of order s is the generalized hexagon of order (s, 1) obtained from Π by putting
equal to the set of all flags of Π, by putting
equal to the set of all points and lines of Π, and where I is the natural incidence relation (inverse containment), i.e., Γ is the dual of the double of Π in the sense of H. Van Maldeghem (1998, “Generalized Polygons,” Birkhäuser Verlag, Basel). Then we say that Γ is fully and weakly embedded in the finite projective space PG(d, q) if Γ is a subgeometry of the natural point-line geometry associated with PG(d, q), if s=q, if the set of points of Γ generates PG(d, q), and if the set of points of Γ not opposite any given point of Γ does not generate PG(d, q). In two earlier papers we have shown that the dimension d of the projective space belongs to {6, 7, 8}, that the projective plane Π is Desarguesian, and we have classified the full and weak embeddings of Γ (Γ as above) in the case that there are two opposite lines L, M of Γ with the property that the subspace UL, M of PG(d, q) generated by all lines of Γ meeting either L or M has dimension 6 (which is automatically satisfied if d=6). In the present paper, we partly handle the case d=7; more precisely, we consider for d=7 the case where for all pairs (L, M) of opposite lines of Γ, the subspace UL, M has dimension 7 and where there exist four lines concurrent with L contained in a 4-dimensional subspace of PG(7, q). 相似文献
15.
Let q=pr with p=3 and r2. We give a recursion formula for the moments of a Kloosterman sum over the finite field , which utilizes known weight formulae for the ternary Melas code M of length q−1. The method is illustrated by giving explicit formulae for the moments up to the tenth moment. As an application for the formulae, and for their analogues obtained earlier in case p=2, we get the exact number of rational points on fibre products of certain Kloosterman curves. As a corollary we obtain identities between Ramanujan's tau-function, Kronecker class numbers, and Dickson polynomials. 相似文献
16.
A. Bir 《Indagationes Mathematicae》2000,11(4):499
Let z1, z2, …, zn be complex numbers, and write
for their power sums. Let
where the minimum is taken under the condition that
. In this paper we prove that
. 相似文献
17.
D. S. Lubinsky 《Journal of Approximation Theory》2002,118(2):153-162
For n1, let {xjn}j=1n be n distinct points and let Ln[·] denote the corresponding Lagrange Interpolation operator. Let W :
→[0,∞). What conditions on the array {xjn}1jn, n1 ensure the existence of p>0 such
for every continuous f :
→
with suitably restricted growth, and some “weighting factor” φb? We obtain a necessary and sufficient condition for such a p to exist. The result is the weighted analogue of our earlier work for interpolation arrays contained in a compact set. 相似文献
Full-size image
18.
In [11], a new bound for the number of points on an algebraic curve over a finite field of odd order was obtained, and applied to improve previous bounds on the size of a complete arc not contained in a conic. Here, a similar approach is used to show that a complete arc in a plane of even order q has size q+2 or
or less than
. To obtain this result, first a new characterization of a Hermitian curve for any square q is given; more precisely, it is shown that a curve of sufficiently low degree has a certain upper bound for the number of its rational points with equality occurring in this bound only when the curve is Hermitian. Finally, another application is given concerning the degree of the curve on which a unital can lie. 相似文献
19.
Let Ω be a region in the complex plane. In this paper we introduce a class of sesquianalytic reproducing kernels on Ω that we call B-kernels. When Ω is the open unit disk
and certain natural additional hypotheses are added we call such kernels k Bergman-type kernels. In this case the associated reproducing kernel Hilbert space
(k) shares certain properties with the classical Bergman space L2α of the unit disk. For example, the weighted Bergman kernels kβw(z)=(1−wz)−β, 1β2 are Bergman-type kernels. Furthermore, for any Bergman-type kernel k one has H2
(k)L2a, where the inclusion maps are contractive, and Mζ, the operator of multiplication with the identity function ζ, defines a contraction operator on
(k). Our main results about Bergman-type kernels k are the following two: First, once properly normalized, the reproducing kernel for any nontrivial zero based invariant subspace
of
(k) is a Bergman-type kernel as well. For the weighted Bergman kernels kβ this result even holds for all
ζ-invariant subspace
of index 1, i.e., whenever the dimension of
/ζ
is one. Second, if
is any multiplier invariant subspace of
(k), and if we set
*=
z
, then Mζ
is unitarily equivalent to Mζ acting on a space of
*-valued analytic functions with an operator-valued reproducing kernel of the type
where V is a contractive analytic function V :
→
(
,
*), for some auxiliary Hilbert space
. Parts of these theorems hold in more generality. Corollaries include contractive divisor, wandering subspace, and dilation theorems for all Bergman-type reproducing kernel Hilbert spaces. When restricted to index one invariant subspaces of
(kβ), 1β2, our approach yields new proofs of the contractive divisor property, the strong contractive divisor property, and the wandering subspace theorems and inner–outer factorization. Our proofs are based on the properties of reproducing kernels, and they do not involve the use of biharmonic Green functions as had some of the earlier proofs. 相似文献
Full-size image
20.
Given a subset E of convex functions from
into
which satisfy growth conditions of order p>1 and an open bounded subset
of
, we establish the continuity of a map μΦμ from the set of all Young measures on
equipped with the narrow topology into a set of suitable functionals defined in
and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization. 相似文献