共查询到20条相似文献,搜索用时 31 毫秒
1.
Jun Wu 《Monatshefte für Mathematik》2006,54(4):259-264
For
log\frac1+?52 £ l* £ l* < ¥{\rm log}\frac{1+\sqrt{5}}{2}\leq \lambda_\ast \leq \lambda^\ast < \infty
, let E(λ*, λ*) be the set
{x ? [0,1): liminfn ? ¥\fraclogqn(x)n=l*, limsupn ? ¥\fraclogqn(x)n=l*}. \left\{x\in [0,1):\ \mathop{\lim\inf}_{n \rightarrow \infty}\frac{\log q_n(x)}{n}=\lambda_{\ast}, \mathop{\lim\sup}_{n \rightarrow \infty}\frac{\log q_n(x)}{n}=\lambda^{\ast}\right\}.
It has been proved in [1] and [3] that E(λ*, λ*) is an uncountable set. In the present paper, we strengthen this result by showing that
dimE(l*, l*) 3 \fracl* -log\frac1+?522l*\dim E(\lambda_{\ast}, \lambda^{\ast}) \ge \frac{\lambda_{\ast} -\log \frac{1+\sqrt{5}}{2}}{2\lambda^{\ast}} 相似文献
2.
Sinan Ünver 《Mathematische Annalen》2010,348(4):833-858
Let ${k[\varepsilon]_{2}:=k[\varepsilon]/(\varepsilon^{2})}Let k[e]2:=k[e]/(e2){k[\varepsilon]_{2}:=k[\varepsilon]/(\varepsilon^{2})} . The single valued real analytic n-polylogarithm
Ln: \mathbbC ? \mathbbR{\mathcal{L}_{n}: \mathbb{C} \to \mathbb{R}} is fundamental in the study of weight n motivic cohomology over a field k, of characteristic 0. In this paper, we extend the construction in ünver (Algebra Number Theory 3:1–34, 2009) to define additive
n-polylogarithms lin:k[e]2? k{li_{n}:k[\varepsilon]_{2}\to k} and prove that they satisfy functional equations analogous to those of Ln{\mathcal{L}_{n}}. Under a mild hypothesis, we show that these functions descend to an analog of the nth Bloch group Bn¢(k[e]2){B_{n}' (k[\varepsilon]_{2})} defined by Goncharov (Adv Math 114:197–318, 1995). We hope that these functions will be useful in the study of weight n motivic cohomology over k[ε]2. 相似文献
3.
Recently, Girstmair and Schoissengeier studied the asymptotic behavior of the arithmetic mean of Dedekind sums
\frac1j(N) ? 0 £ m < Ngcd(m,N)=1 |S(m,N)|\frac{1}{\varphi(N)} \sum_{\mathop{\mathop{ 0 \le m< N}}\limits_{\gcd(m,N)=1}} \vert S(m,N)\vert
, as N → ∞. In this paper we consider the arithmetic mean of weighted differences of Dedekind sums in the form
Ah(Q)=\frac1?\fracaq ? FQh(\fracaq) ×?\fracaq ? FQh(\fracaq) |s(a¢,q¢)-s(a,q)|A_{h}(Q)=\frac{1}{\sum_{\frac{a}{q} \in {\cal F}_{Q}}h\left(\frac{a}{q}\right)} \times \sum_{\frac{a}{q} \in {\cal F}_{\!Q}}h\left(\frac{a}{q}\right) \vert s(a^{\prime},q^{\prime})-s(a,q)\vert
, where
h:[0,1] ? \Bbb Ch:[0,1] \rightarrow {\Bbb C}
is a continuous function with
ò01 h(t) d t 1 0\int_0^1 h(t) \, {\rm d} t \ne 0
,
\fracaq{\frac{a}{q}}
runs over
FQ{\cal F}_{\!Q}
, the set of Farey fractions of order Q in the unit interval [0,1] and
\fracaq < \fraca¢q¢{\frac{a}{q}}<\frac{a^{\prime}}{q^{\prime}}
are consecutive elements of
FQ{\cal F}_{\!Q}
. We show that the limit lim
Q→∞
A
h
(Q) exists and is independent of h. 相似文献
4.
E. Gečiauskas 《Geometriae Dedicata》2006,121(1):9-18
We have obtained a recurrence formula $I_{n+3} = \frac{4(n+3)}{\pi(n+4)}VI_{n+1}We have obtained a recurrence formula
In+3 = \frac4(n+3)p(n+4)VIn+1I_{n+3} = \frac{4(n+3)}{\pi(n+4)}VI_{n+1} for integro-geometric moments in the case of a circle with the area V, where
In = ò\nolimitsK ?Gsnd GI_n = \int \nolimits_{K \cap G}\sigma^{n}{\rm d} G, while in the case of a convex domain K with the perimeter S and area V the recurrence formula
In+3 = \frac8(n+3)V2(n+1)(n+4)p[\fracd In+1d V - \fracIn+1S \fracd Sd V ] I_{n+3} = \frac{8(n+3)V^2}{(n+1)(n+4)\pi}\Big[\frac{{\rm d} I_{n+1}}{{\rm d} V} - \frac{I_{n+1}}{S} \frac{{\rm d} S}{{\rm d} V} \Big] 相似文献
5.
Y. C. Wang 《Acta Mathematica Hungarica》2012,135(3):248-269
Let Hk\mathcal{H}_{k} denote the set {n∣2|n,
n\not o 1 (mod p)n\not\equiv 1\ (\mathrm{mod}\ p) ∀ p>2 with p−1|k}. We prove that when
X\frac1120(1-\frac12k) +e\leqq H\leqq XX^{\frac{11}{20}\left(1-\frac{1}{2k}\right) +\varepsilon}\leqq H\leqq X, almost all integers
n ? \allowbreak Hk ?(X, X+H]n\in\allowbreak {\mathcal{H}_{k} \cap (X, X+H]} can be represented as the sum of a prime and a k-th power of prime for k≧3. Moreover, when
X\frac1120(1-\frac1k) +e\leqq H\leqq XX^{\frac{11}{20}\left(1-\frac{1}{k}\right) +\varepsilon}\leqq H\leqq X, almost all integers n∈(X,X+H] can be represented as the sum of a prime and a k-th power of integer for k≧3. 相似文献
6.
7.
Dani Szpruch 《The Ramanujan Journal》2011,26(1):45-53
Let
\mathbbF\mathbb{F} be a p-adic field, let χ be a character of
\mathbbF*\mathbb{F}^{*}, let ψ be a character of
\mathbbF\mathbb{F} and let gy-1\gamma_{\psi}^{-1} be the normalized Weil factor associated with a character of second degree. We prove here that one can define a meromorphic
function [(g)\tilde](c,s,y)\widetilde{\gamma}(\chi ,s,\psi) via a similar functional equation to the one used for the definition of the Tate γ-factor replacing the role of the Fourier transform with an integration against y·gy-1\psi\cdot\gamma_{\psi}^{-1}. It turns out that γ and [(g)\tilde]\widetilde{\gamma} have similar integral representations. Furthermore, [(g)\tilde]\widetilde{\gamma} has a relation to Shahidi‘s metaplectic local coefficient which is similar to the relation γ has with (the non-metalpectic) Shahidi‘s local coefficient. Up to an exponential factor, [(g)\tilde](c,s,y)\widetilde{\gamma}(\chi,s,\psi) is equal to the ratio
\fracg(c2,2s,y)g(c,s+\frac12,y)\frac{\gamma(\chi^{2},2s,\psi)}{\gamma(\chi,s+\frac{1}{2},\psi)}. 相似文献
8.
Jaume Llibre Clàudia Valls 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(5):657-679
In this paper we classify the centers localized at the origin of coordinates, the cyclicity of their Hopf bifurcation and
their isochronicity for the polynomial differential systems in
\mathbbR2{\mathbb{R}^2} of degree d that in complex notation z = x + i
y can be written as
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