Arithmetic Properties of Euler-Type Series with a Liouvillian Polyadic Parameter

Doklady Mathematics - This paper states that, for any nonzero linear form $${{h}_{0}}{{f}_{0}}(1) + {{h}_{1}}{{f}_{1}}(1)$$ with integer coefficients h0, h1, there exist infinitely many p-adic...     

On the Values of Heine Series at Algebraic Points

The paper considers linear independence measures of the values of certain q–hypergeometric series and their derivatives at algebraic points. The results are given both in the archimedean and p–adic case.     

Fast Parallel Method for Polynomial Evaluation at Points in Arithmetic Progression

We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into rn new ones and evaluating the polynomial at each point of these new progressions recursively, this method saves most of the multiplications in the price of little increase of additions comparing to Horner＇s method, while their accuracy are almost the same. We also introduce vector structure to the recursive process making it suitable for parallel applications.     

Discontinuity Points of Separately Continuous Mappings with at Most Countable Set of Values

Ukrainian Mathematical Journal - We obtain a general result on the constancy of separately continuous mappings and their analogs, which yields the well-known Sierpiński theorem. By using this...     

代数系数幂级数在超越数上值的代数无关性

本文证明了一类具有代数系数的幂级数在超越数上值约代数无关性．     

Fourier-Laplace级数的缺项算术平均在Lebesgue点处的收敛性

设f(x)为定义于n-维欧氏空间R~n中的单位球面∑(n-1)上的Lebesgue可积函数,σ_N~δ(f)表示f的Fourier-Laplace级数的Cesaro平均.众所周知,λ:=(n-2)/2是Cesaro平均的临界阶.本文就n是偶数的情形证明了,使得1/N∑_(k=1)~Nσ_(n_k)~λ(f)(x)→f(x),N→∞,在每个满足一定对极条件的Lebesgue点成立的具有一定“缺项程度”的数列{n_k}的存在性。     

Summability of Fourier-Laplace Series with the Method of Lacunary Arithmetical Means at Lebesgue Points

Let ∑ _{n −1} be the unit sphere in the n-dimensional Euclidean space ℝ ⁿ . For a funcion ƒ∈L(∑ _{n −1}) denote by σ^δ _N (ƒ) the Cesàro means of order δ of the Fourier-Laplace series of ƒ. The special value of δ is known as the critical index. In the case when n is even, this paper proves the existence of the ‘rare’ sequence {n _k } such that the summability takes place at each Lebesgue point satisfying some antipole conditions. Received June 28, 1999, Revised August 11, 1999, Accepted February 16, 2000     

On Critical Values of Polynomials with Real Critical Points

Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′ are real. We show that there is a zero ζ of f′ such that |f(ζ)/ζ|≤2/3, and that this inequality can be taken to be strict unless f is of the form f(z)=z+cz ³.     

Multiple Complete Rational Arithmetic Sums of Polynomial Values

For multiple arithmetic rational sums of a special form, bounds with reduction equal to the square root of the length of the summation interval of the complete sum are found. The paper continues the study begun in [1–12].     

Continued Fractions which Correspond to Power Series Expansions at Two Points

Theoretical results are derived for constructing continued fractionswhich correspond, in some prescribed way, to given power seriesexpansions at two points. In those cases where the two powerseries are expansions of the same function, new approximationsto the functions are obtained. Error estimates for such rationalfunction approximations are developed in certain cases. Someexamples are given.     

Effect of Islands in Diffusive Properties of the Standard Map for Large Parameter Values

Foundations of Computational Mathematics - In this paper we review, based on massive, long-term, numerical simulations, the effect of islands on the statistical properties of the standard map for...     

算术图的若干性质

本文得到了算术图的一些新性质，并解决了文[1]提出的两个猜想.     

虚二次域的L-函数在中心点的值

给出了虚二次数域的一类L-函数在中心点的值,这为研究Dirichlet L-函数在中心点的算术意义提供了一条新的途径.     

Large Values of Eigenfunctions on Arithmetic Hyperbolic 3-Manifolds

We prove that, on a distinguished class of arithmetic hyperbolic 3-manifolds, there is a sequence of L ²-normalized high-energy Hecke–Maass eigenforms f_j{phi_{j}} which achieve values as large as l^1/4+o(1)_j{lambda^{1/4+o(1)}_{j}}, where ( D+l_j ) f_j = 0{( Delta+lambda_{j} ) phi_{j} = 0}. Arithmetic hyperbolic 3-manifolds on which this exceptional behavior is exhibited are, up to commensurability, precisely those containing immersed totally geodesic surfaces. We adapt the method of resonators and connect values of eigenfunctions to the global geometry of the manifold by employing the pre-trace formula and twists by Hecke correspondences. Automorphic representations corresponding to forms appearing with highest weights in the optimized spectral averages are characterized both in terms of base change lifts and in terms of theta lifts from GSp₂.     

含参变量富里叶级数的Laplace变换求和法

本文建立了含参变量富里叶级数的Laplace变换求和定理.利用Laplace变换表可以求得许多在力学上有重要应用的新的含参变量富里叶级数的和式.     

Arithmetic Properties of Summands of Partitions

Let d d, d2 2. We prove that for almost all partitions of an integer the parts are well distributed in residue classes mod d. The limitations of the uniformity of this distribution are also studied.     

On Locally Repeated Values of Certain Arithmetic Functions,IV

Let (n) denote the number of prime divisors of n and let (n) denote the number of prime power divisors of n. We obtain upper bounds for the lengths of the longest intervals below x where (n), respectively (n), remains constant. Similarly we consider the corresponding problems where the numbers (n), respectively (n), are required to be all different on an interval. We show that the number of solutions g(n) to the equation m+(m)=n is an unbounded function of n, thus answering a question posed in an earlier paper in this series. A principal tool is a Turán-Kubilius type inequality for additive functions on arithmetic progressions with a large modulus.     

Properties of Some Generalized Hypergeometric Functions Governing Coupling at Transition Points

Understanding of wave propagation problems is enhanced by consideringgeneralizations to differential equations of order 2n. In particular,reflection and coupling of waves at transition points can involvecertain types of generalized hypergeometric functions. In thispaper, properties of _oF_2n-1 functions are considered systematically,when the parameters are specially chosen for application totransition points; a wide range of interesting properties unfolds,which recall the properties of Bessel functions when n = 1.