共查询到20条相似文献,搜索用时 0 毫秒
1.
H. Inoue Sh. Kamada K. Naito 《P-Adic Numbers, Ultrametric Analysis, and Applications》2016,8(4):312-324
In this paper we construct the multi-dimensional p-adic approximation lattices by using simultaneous approximation problems (SAP) of p-adic numbers and we estimate the l ∞ norm of the p-adic SAP solutions theoretically by applying Dirichlet’s principle and numerically by using the LLL algorithm. By using the SAP solutions as private keys, the security of which depends on NP-hardness of SAP or the shortest vector problems (SVP) of p-adic lattices, we propose a p-adic knapsack cryptosystem with commitment schemes, in which the sender Alice prepares ciphertexts and the verification keys in her p-adic numberland. 相似文献
2.
Sergio Albeverio Sergei V. Kozyrev 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(1):21-34
We discuss transformation of p-adic pseudodifferential operators (in the one-dimensional and multidimensional cases) with respect to p-adic maps which correspond to automorphisms of the tree of balls in the corresponding p-adic spaces. In the dimension one we find a rule of transformation for pseudodifferential operators. In particular we find
the formula of pseudodifferentiation of a composite function with respect to the Vladimirov p-adic fractional operator. We describe the frame of wavelets for the group of parabolic automorphisms of the tree T (O
p
) of balls in O
p
. In many dimensions we introduce the group of mod p-affine transformations, the family of pseudodifferential operators corresponding to pseudodifferentiation along vector fields
on the tree T (O
p
) and obtain a rule of transformation of the introduced pseudodifferential operators with respect to mod p-affine transformations. 相似文献
3.
Jyoti Prakash Saha 《The Ramanujan Journal》2017,43(2):359-369
Let the function \(s_g\) map a positive integer to the sum of its digits in the base g. A number k is called n-flimsy in the base g if \(s_g(nk)<s_g(k)\). Clearly, given a base g, \(g\geqslant 2\), if n is a power of g, then there does not exist an n-flimsy number in the base g. We give a constructive proof of the existence of an n-flimsy number in the base g for all the other values of n (such an existence follows from the results of Schmidt and Steiner, but the explicit construction is a novelty). Our algorithm for construction of such a number, say k, is very flexible in the sense that, by easy modifications, we can impose further requirements on k—k ends with a given sequence of digits, k begins with a given sequence of digits, k is divisible by a given number (or belongs to a certain congruence class modulo a given number), etc. 相似文献
4.
Lennart Gehrmann 《Israel Journal of Mathematics》2018,226(1):237-294
We use modular symbols to construct p-adic L-functions for cohomological cuspidal automorphic representations on GL(2n), which admit a Shalika model. Our construction differs from former ones in that it systematically makes use of the representation theory of p-adic groups. 相似文献
5.
For a newform f for Γ0(N) of even weight k supersingular at a prime p ≥ 5, by using infinite dimensional p-adic analysis, we prove that the p-adic L-function L
p
(f,α; χ) has finite order of vanishing at any character of the form [(c)\tilde] s ( x ) = xs\tilde \chi _s \left( x \right) = x^s. In particular, under the natural embedding of ℤ
p
in the group of ℂ*
p
-valued continuous characters of ℤ*
p
, the order of vanishing at any point is finite. 相似文献
6.
B. G. Dragovich 《Theoretical and Mathematical Physics》2010,164(3):1151-1155
We consider the construction of Lagrangians that might be suitable for describing the entire p-adic sector of an adelic open
scalar string. These Lagrangians are constructed using the Lagrangian for p-adic strings with an arbitrary prime number p.
They contain space-time nonlocality because of the d’Alembertian in the argument of the Riemann zeta function. We present
a brief review and some new results. 相似文献
7.
Mihran Papikian 《manuscripta mathematica》2008,127(3):397-410
We study the eigenvalues of the p-adic curvature transformationson buildings. In particular, we determine the maximal eigenvalues ofthese transformations. 相似文献
8.
Sergio Albeverio Sergei V. Kozyrev 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(4):265-277
The approach to p-adic wavelet theory from the point of view of representation theory is discussed. p-Adic wavelet frames can be constructed as orbits of some p-adic groups of transformations. These groups are automorphisms of the tree of balls in the p-adic space. In the present paper we consider deformations of the standard p-adic metric in many dimensions and construct some corresponding groups of transformations. We build several examples of p-adic wavelet bases. We show that the constructed wavelets are eigenvectors of some pseudodifferential operators. 相似文献
9.
Kamal Boussaf 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(4):285-292
We investigate Picard-Hayman behavior of derivatives of meromorphic functions on an algebraically closed field K, complete with respect to a non-trivial ultrametric absolute value. We present an analogue of the well-known Hayman’s alternative
theorem both in K and in any open disk. Here the main hypothesis is based on the behaviour of |f|(r) when r tends to +∞ on properties of special values and quasi-exceptional values.We apply this study to give some sufficient conditions
on meromorphic functions so that they satisfy Hayman’s conjectures for n = 1and for n = 2. Given a meromorphic transcendental function f, at least one of the two functions f′f and f′f
2 assumes all non-zero values infinitely often. Further, we establish that if the sequence of residues at simple poles of a
meromorphic transcendental function on K admits no infinite stationary subsequence, then either f′ + af
2 has infinitely many zeros that are not zeros of f for every a ∈ K* or both f′ + bf
3 and f′ + bf
4 have infinitely many zeros that are not zeros of f for all b ∈ K*. Most of results have a similar version for unbounded meromorphic functions inside an open disk. 相似文献
10.
S. S. Volosivets 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(3):252-259
p-Adic analogs of Hausdorff operator are introduced. Sufficient conditions of its boundedness in p-adic Hardy and BMO spaces are given. The Titchmarsh-type theorem about commuting relations between Hausdorff operator, its conjugate and p-adic Fourier transform is established. 相似文献
11.
L. F. Chacón-Cortés Andrés Vargas 《P-Adic Numbers, Ultrametric Analysis, and Applications》2017,9(3):183-196
The problem of existence of solutions to p-adic semilinear heat equations with particular nonlinear terms has already been studied in the literature but the occurrence of blow-up phenomena has not been considered yet. We initiate the study of finite time blow-up for solutions of this kind of p-adic semilinear equations, proving that this phenomenon always arises under appropriate assumptions in the case when the exponent of nonlinearity times the dimension is strictly less than the order of the operator. 相似文献
12.
Florian Herzig 《Inventiones Mathematicae》2011,186(2):373-434
Let F be a finite extension of ℚ
p
. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} to be supersingular. We then give the classification of irreducible admissible smooth GL
n
(F)-representations over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel–Livné for n=2. For general split reductive groups we obtain similar results under stronger hypotheses. 相似文献
13.
Pavel Trojovský 《P-Adic Numbers, Ultrametric Analysis, and Applications》2017,9(3):228-235
Let (F n ) n≥0 be the Fibonacci sequence. For 1 ≤ k ≤ m, the Fibonomial coefficient is defined as . In 2013, Marques, Sellers and Trojovský proved that if p is a prime number such that p ≡ ±2 (mod 5), then \(p{\left| {\left[ {\begin{array}{*{20}{c}} {{p^{a + 1}}} \\ {{p^a}} \end{array}} \right]} \right._F}\) for all integers a ≥ 1. In 2015, Marques and Trojovský worked on the p-adic order of \({\left[ {\begin{array}{*{20}{c}} {{p^{a + 1}}} \\ {{p^a}} \end{array}} \right]_F}\) for all a ≥ 1 when p ≠ 5. In this paper, we shall provide the exact p-adic order of \({\left[ {\begin{array}{*{20}{c}} {{p^{a + 1}}} \\ {{p^a}} \end{array}} \right]_F}\) for all integers a, b ≥ 1 and for all prime number p.
相似文献
$${\left[ {\begin{array}{*{20}{c}} m \\ k \end{array}} \right]_F} = \frac{{{F_{m - k + 1}} \cdots {F_{m - 1}}{F_m}}}{{{F_1} \cdots {F_k}}}$$
14.
Wei Cao 《Discrete and Computational Geometry》2011,45(3):522-528
Let f(X) be a polynomial in n variables over the finite field
\mathbbFq\mathbb{F}_{q}. Its Newton polytope Δ(f) is the convex closure in ℝ
n
of the origin and the exponent vectors (viewed as points in ℝ
n
) of monomials in f(X). The minimal dilation of Δ(f) such that it contains at least one lattice point of $\mathbb{Z}_{>0}^{n}$\mathbb{Z}_{>0}^{n} plays a vital pole in the p-adic estimate of the number of zeros of f(X) in
\mathbbFq\mathbb{F}_{q}. Using this fact, we obtain several tight and computational bounds for the dilation which unify and improve a number of previous
results in this direction. 相似文献
15.
Mikhail V. Dolgopolov Alexander P. Zubarev 《P-Adic Numbers, Ultrametric Analysis, and Applications》2011,3(1):39-51
In this paper we consider a generalization of analysis on p-adic numbers field to the m case of m-adic numbers ring. The basic statements, theorems and formulas of p-adic analysis can be used for the case of m-adic analysis without changing. We discuss basic properties of m-adic numbers and consider some properties of m-adic integration and m-adic Fourier analysis. The class of infinitely divisible m-adic distributions and the class of m-adic stochastic Levi processes were introduced. The special class of m-adic CTRW process and fractional-time m-adic random walk as the diffusive limit of it is considered. We found the asymptotic behavior of the probability measure
of initial distribution support for fractional-time m-adic random walk. 相似文献
16.
We study the Möbius invariant spacesQ p andQ p, 0 of analytic functions. These scales of spaces include BMOA=Q1, VMOA=Q1, 0 and the Dirichlet space=Q0. Using the Bergman metric, we establish decomposition theorems for these spaces. We obtain also a fractional derivative characterization for bothQ p andQ p, 0 . 相似文献
17.
Let G be an infinite finitely generated pro-p group acting on a pro-p tree such that the restriction of the action to some open subgroup is free. We prove that G splits over an edge stabilizer either as an amalgamated free pro-p product or as a pro-p \({\text {HNN}}\)-extension. Using this result, we prove under a certain condition that free pro-p products with procyclic amalgamation inherit from its amalgamated free factors the property of each 2-generated pro-p subgroup being free pro-p. This generalizes known pro-p results, as well as some pro-p analogues of classical results in abstract combinatorial group theory. 相似文献
18.
B. Dragovich 《Theoretical and Mathematical Physics》2010,163(3):768-773
We study the construction of Lagrangians that can be considered the Lagrangians of the p-adic sector of an adelic open scalar
string. Such Lagrangians are closely related to the Lagrangian for a single p-adic string and contain the Riemann zeta function
with the d’Alembertian in its argument. In particular, we present a new Lagrangian obtained by an additive approach that combines
all p-adic Lagrangians. This new Lagrangian is attractive because it is an analytic function of the d’Alembertian. Investigating
the field theory with the Riemann zeta function is also interesting in itself. 相似文献
19.
An S-arithmetic Khintchine-type theorem for products of non-degenerate analytic p-adic manifolds is proved for the convergence case. In the p-adic case the divergence part is also obtained. 相似文献
20.
A. Kh. Khudoyberdiyev T. K. Kurbanbaev B. A. Omirov 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(3):207-221
The present paper is devoted to the study of low dimensional Leibniz algebras over the field of p-adic numbers. The classification up to isomorphism of three-dimensional Lie algebras over the integer p-adic numbers is already known [8]. Here, we extend this classification to solvable Lie and non-Lie Leibniz algebras over
the field of p-adic numbers. 相似文献