共查询到20条相似文献,搜索用时 15 毫秒
1.
Paul D. Nelson 《The Ramanujan Journal》2012,27(2):235-284
Let
\mathbbF\mathbb{F} be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on
\operatornameGL2/\mathbbF\operatorname{GL}_{2}/\mathbb{F} of weight
(k1,?,k[\mathbbF:\mathbbQ])(k_{1},\ldots,k_{[\mathbb{F}:\mathbb{Q}]}), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as
max(k1,?,k[\mathbbF:\mathbbQ]) ? ¥\max(k_{1},\ldots,k_{[\mathbb{F}:\mathbb{Q}]}) \rightarrow \infty. 相似文献
2.
We describe the dynamics of an arbitrary affine dynamical system on a local field by exhibiting all its minimal subsystems.
In the special case of the field
\mathbbQp{\mathbb{Q}_p} of p-adic numbers, for any non-trivial affine dynamical system, we prove that the field
\mathbbQp{\mathbb{Q}_p} is decomposed into a countable number of invariant balls or spheres each of which consists of a finite number of minimal
subsets. Consequently, we give a complete classification of topological conjugacy for non-trivial affine dynamics on
\mathbbQp{\mathbb{Q}_p} . For each given prime p, there is a finite number of conjugacy classes. 相似文献
3.
Cristina Fernández-Córdoba Jaume Pujol Mercè Villanueva 《Designs, Codes and Cryptography》2010,56(1):43-59
A code C{{\mathcal C}} is
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C{{\mathcal C}} by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). The corresponding binary codes of
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-additive codes under an extended Gray map are called
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes. In this paper, the invariants for
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the rank and dimension of the kernel, are studied. Specifically, given the algebraic parameters of
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the possible values of these two invariants, giving lower and upper bounds, are established. For each possible
rank r between these bounds, the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with dimension of the kernel k is given. Finally, the bounds on the rank, once the kernel dimension is fixed, are established and the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code for each possible pair (r, k) is given. 相似文献
4.
Swarnendu Datta 《Transformation Groups》2010,15(1):72-91
Let G be a commutative, unipotent, perfect, connected group scheme over an algebraically closed field of characteristic p > 0 and let E be a biextension of G × G by the discrete group
\mathbbQp/\mathbbZp\mathbb{Q}_{p}/\mathbb{Z}_{p}. When E is skew-symmetric, V. Drinfeld defined a certain metric group A associated to E (when G is the perfectization of the additive group
\mathbbGa\mathbb{G}_{a}, it is easy to compute this metric group, cf. Appendix A). In this paper we prove a conjecture due to Drinfeld about the
class of the metric group A in the Witt group (cf. Appendix B). 相似文献
5.
6.
Fractional Moments of Automorphic L-Functions on GL(m) 总被引:1,自引:1,他引:0
Qinghua PI 《数学年刊B辑(英文版)》2011,32(4):631-642
Let π be an irreducible unitary cuspidal representation of GLm(AQ), m ≥ 2.
Assume that π is self-contragredient. The author gets upper and lower bounds of the same
order for fractional moments of automorphic L-function L(s, π) on the critical line under
Generalized Ramanujan Conjecture; the upper bound being conditionally subject to the
truth of Generalized Riemann Hypothesis. 相似文献
7.
Andrea Bonfiglioli 《Archiv der Mathematik》2009,93(3):277-286
Let ${\mathbb{G}}Let
\mathbbG{\mathbb{G}} be a Carnot group of step r and m generators and homogeneous dimension Q. Let
\mathbbFm,r{\mathbb{F}_{m,r}} denote the free Lie group of step r and m generators. Let also
p:\mathbbFm,r?\mathbbG{\pi:\mathbb{F}_{m,r}\to\mathbb{G}} be a lifting map. We show that any horizontally convex function u on
\mathbbG{\mathbb{G}} lifts to a horizontally convex function u°p{u\circ \pi} on
\mathbbFm,r{\mathbb{F}_{m,r}} (with respect to a suitable horizontal frame on
\mathbbFm,r{\mathbb{F}_{m,r}}). One of the main aims of the paper is to exhibit an example of a sub-Laplacian L=?j=1m Xj2{\mathcal{L}=\sum_{j=1}^m X_j^2} on a Carnot group of step two such that the relevant L{\mathcal{L}}-gauge function d (i.e., d
2-Q
is the fundamental solution for L{\mathcal{L}}) is not h-convex with respect to the horizontal frame {X
1, . . . , X
m
}. This gives a negative answer to a question posed in Danielli et al. (Commun. Anal. Geom. 11 (2003), 263–341). 相似文献
8.
Commutative congruence-simple semirings have already been characterized with the exception of the subsemirings of ℝ+. Even the class
CongSimp(\mathbb Q+)\mathit{\mathcal{C}ong\mathcal{S}imp}(\mathbb {Q}^{+}) of all congruence-simple subsemirings of ℚ+ has not been classified yet. We introduce a new large class of the congruence-simple saturated subsemirings of ℚ+. We classify all the maximal elements of
CongSimp(\mathbbQ+)\mathit{\mathcal{C}ong\mathcal {S}imp}(\mathbb{Q}^{+}) and show that every element of
CongSimp(\mathbbQ+)\{\mathbbQ+}\mathit{\mathcal{C}ong\mathcal{S}imp}(\mathbb{Q}^{+})\setminus\{\mathbb{Q}^{+}\} is contained in at least one of them. 相似文献
9.
Yolanda Fuertes 《Archiv der Mathematik》2010,95(1):15-18
Mestre has shown that if a hyperelliptic curve C of even genus is defined over a subfield
k ì \mathbbC{k \subset \mathbb{C}} then C can be hyperelliptically defined over the same field k. In this paper, for all genera g > 1, g o 1{g\equiv1} mod 4, hence odd, we construct an explicit hyperelliptic curve defined over
\mathbbQ{\mathbb{Q}} which can not be hyperelliptically defined over
\mathbbQ{\mathbb{Q}}. 相似文献
10.
Alexander N. Dranishnikov Yuli B. Rudyak 《Journal of Fixed Point Theory and Applications》2009,6(1):165-177
It follows from a theorem of Gromov that the stable systolic category catstsys M{\rm cat}_{\rm stsys} M of a closed manifold M is bounded from below by
cl\mathbbQ M{\rm cl}_{\mathbb{Q}} M, the rational cup-length of M [Ka07]. We study the inequality in the opposite direction. In particular, combining our results with Gromov’s theorem, we
prove the equality
catstsys M = cl\mathbbQ M{\rm cat}_{\rm stsys} M = {\rm cl}_{\mathbb{Q}} M for simply connected manifolds of dimension ≤ 7. 相似文献
11.
Clément de Seguins Pazzis 《Archiv der Mathematik》2010,95(4):333-342
When
\mathbbK{\mathbb{K}} is an arbitrary field, we study the affine automorphisms of
Mn(\mathbbK){{\rm M}_n(\mathbb{K})} that stabilize
GLn(\mathbbK){{\rm GL}_n(\mathbb{K})}. Using a theorem of Dieudonné on maximal affine subspaces of singular matrices, this is easily reduced to the known case
of linear preservers when n > 2 or # ${\mathbb{K} > 2}${\mathbb{K} > 2}. We include a short new proof of the more general Flanders theorem for affine subspaces of
Mp,q(\mathbbK){{\rm M}_{p,q}(\mathbb{K})} with bounded rank. We also find that the group of affine transformations of
M2(\mathbbF2){{\rm M}_2(\mathbb{F}_2)} that stabilize
GL2(\mathbbF2){{\rm GL}_2(\mathbb{F}_2)} does not consist solely of linear maps. Using the theory of quadratic forms over
\mathbbF2{\mathbb{F}_2}, we construct explicit isomorphisms between it, the symplectic group
Sp4(\mathbbF2){{\rm Sp}_4(\mathbb{F}_2)} and the symmetric group
\mathfrakS6{\mathfrak{S}_6}. 相似文献
12.
V. V. Lebedev 《Functional Analysis and Its Applications》2012,46(2):121-132
We consider the space
A(\mathbbT)A(\mathbb{T}) of all continuous functions f on the circle
\mathbbT\mathbb{T} such that the sequence of Fourier coefficients
[^(f)] = { [^(f)]( k ), k ? \mathbbZ }\hat f = \left\{ {\hat f\left( k \right), k \in \mathbb{Z}} \right\} belongs to l
1(ℤ). The norm on
A(\mathbbT)A(\mathbb{T}) is defined by
|| f ||A(\mathbbT) = || [^(f)] ||l1 (\mathbbZ)\left\| f \right\|_{A(\mathbb{T})} = \left\| {\hat f} \right\|_{l^1 (\mathbb{Z})}. According to the well-known Beurling-Helson theorem, if
f:\mathbbT ? \mathbbT\phi :\mathbb{T} \to \mathbb{T} is a continuous mapping such that
|| einf ||A(\mathbbT) = O(1)\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = O(1), n ∈ ℤ then φ is linear. It was conjectured by Kahane that the same conclusion about φ is true under the assumption that
|| einf ||A(\mathbbT) = o( log| n | )\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\log \left| n \right|} \right). We show that if $\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right)$\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right), then φ is linear. 相似文献
13.
We determine which singular del Pezzo surfaces are equivariant compactifications of
\mathbbG\texta2 \mathbb{G}_{\text{a}}^2 , to assist with proofs of Manin’s conjecture for such surfaces. Additionally, we give an example of a singular quartic del
Pezzo surface that is an equivariant compactification of
\mathbbG\texta {\mathbb{G}_{\text{a}}} ⋊
\mathbbG\textm {\mathbb{G}_{\text{m}}} . Bibliography: 32 titles. 相似文献
14.
Laura Paladino 《Annali di Matematica Pura ed Applicata》2010,189(1):17-23
Let ${\mathcal{E}}Let E{\mathcal{E}} be an elliptic curve defined over
\mathbbQ{\mathbb{Q}} . Let
P ? E(\mathbb Q){P\in {\mathcal{E}}(\mathbb {Q})} and let q be a positive integer. Assume that for almost all valuations
v ? \mathbbQ{v\in \mathbb{Q}} , there exist points
Dv ? E(\mathbb Qv){D_v\in {\mathcal{E}}(\mathbb {Q}_v)} such that P = qD
v
. Is it possible to conclude that there exists a point
D ? E(\mathbb Q){D\in {\mathcal{E}}(\mathbb {Q})} such that P = qD? A full answer to this question is known when q is a power of almost all primes
p ? \mathbbN{p\in \mathbb{N}} , but some cases remain open when p ? S={2,3,5,7,11,13,17,19,37,43,67,163}{p\in S=\{2,3,5,7,11,13,17,19,37,43,67,163\}} . We now give a complete answer in the case when q = 4. 相似文献
15.
We use properties of small resolutions of the ordinary double point in dimension three to construct smooth non-liftable Calabi-Yau
threefolds. In particular, we construct a smooth projective Calabi-Yau threefold over
\mathbbF3{\mathbb{F}_3} that does not lift to characteristic zero and a smooth projective Calabi-Yau threefold over
\mathbbF5{\mathbb{F}_5} having an obstructed deformation. We also construct many examples of smooth Calabi-Yau algebraic spaces over
\mathbbFp{\mathbb{F}_p} that do not lift to algebraic spaces in characteristic zero. 相似文献
16.
A concrete category
\mathbb Q\mathbb {Q} is finite-to-finite (algebraically) almost universal if the category of graphs and graph homomorphisms can be embedded into
\mathbb Q\mathbb {Q} in such a way that finite
\mathbb Q\mathbb {Q}-objects are assigned to finite graphs and non-constant
\mathbb Q\mathbb {Q}-morphisms between any
\mathbb Q\mathbb {Q}-objects assigned to graphs are exactly those arising from graph homomorphisms. A quasivariety
\mathbb Q\mathbb {Q} of algebraic systems of a finite similarity type is Q-universal if the lattice of all subquasivarieties of any quasivariety
\mathbb R\mathbb {R} of algebraic systems of a finite similarity type is isomorphic to a quotient lattice of a sublattice of the subquasivariety
lattice of
\mathbb Q\mathbb {Q}. This paper shows that any finite-to-finite (algebraically) almost universal quasivariety
\mathbb Q\mathbb {Q} of a finite type is Q-universal. 相似文献
17.
Let K be an algebraically closed field of characteristic 0. We conclude the classification of finite-dimensional pointed Hopf algebras
whose group of group-likes is
\mathbbS4\mathbb{S}_4. We also describe all pointed Hopf algebras over
\mathbbS5\mathbb{S}_5 whose infinitesimal braiding is associated to the rack of transpositions. 相似文献
18.
S. V. Hudzenko 《Ukrainian Mathematical Journal》2010,62(7):1158-1162
We consider a semigroup
FP\textfin+ ( \mathfrakS\textfin( \mathbbN ) ) FP_{\text{fin}}^{+} \left( {{\mathfrak{S}_{\text{fin}}}\left( \mathbb{N} \right)} \right) defined as a finitary factor power of a finitary symmetric group of countable order. It is proved that all automorphisms
of
FP\textfin+ ( \mathfrakS\textfin( \mathbbN ) ) FP_{\text{fin}}^{+} \left( {{\mathfrak{S}_{\text{fin}}}\left( \mathbb{N} \right)} \right) are induced by permutations from
\mathfrakS( \mathbbN ) \mathfrak{S}\left( \mathbb{N} \right) . 相似文献
19.
Takuro Fukunaga 《Graphs and Combinatorics》2011,27(5):647-659
An undirected graph G = (V, E) is called
\mathbbZ3{\mathbb{Z}_3}-connected if for all
b: V ? \mathbbZ3{b: V \rightarrow \mathbb{Z}_3} with ?v ? Vb(v)=0{\sum_{v \in V}b(v)=0}, an orientation D = (V, A) of G has a
\mathbbZ3{\mathbb{Z}_3}-valued nowhere-zero flow
f: A? \mathbbZ3-{0}{f: A\rightarrow \mathbb{Z}_3-\{0\}} such that ?e ? d+(v)f(e)-?e ? d-(v)f(e)=b(v){\sum_{e \in \delta^+(v)}f(e)-\sum_{e \in \delta^-(v)}f(e)=b(v)} for all v ? V{v \in V}. We show that all 4-edge-connected HHD-free graphs are
\mathbbZ3{\mathbb{Z}_3}-connected. This extends the result due to Lai (Graphs Comb 16:165–176, 2000), which proves the
\mathbbZ3{\mathbb{Z}_3}-connectivity for 4-edge-connected chordal graphs. 相似文献
20.
Giovanni Di Lena Davide Franco Mario Martelli Basilio Messano 《Mediterranean Journal of Mathematics》2011,8(4):473-489
The main purpose of this paper is to investigate dynamical systems
F : \mathbbR2 ? \mathbbR2{F : \mathbb{R}^2 \rightarrow \mathbb{R}^2} of the form F(x, y) = (f(x, y), x). We assume that
f : \mathbbR2 ? \mathbbR{f : \mathbb{R}^2 \rightarrow \mathbb{R}} is continuous and satisfies a condition that holds when f is non decreasing with respect to the second variable. We show that for every initial condition x0 = (x
0, y
0), such that the orbit
O(x0) = {x0, x1 = F(x0), x2 = F(x1), . . . }, O({\rm{x}}_0) = \{{\rm{x}}_0, {\rm{x}}_1 = F({\rm{x}}_0), {\rm{x}}_2 = F({\rm{x}}_1), . . . \}, 相似文献
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