关于指数丢番图方程a~x+(3a~2-1)~y=(4a~2-1)~z的正整数解(英文)

本文通过计算Jacobi符号,运用代数数的对数线性型的下界估计,证明了:当整数a>1时,指数丢番图方程a~x+(3a~2-1)~y=(4a~2-1)~z仅有正整数解(x,y,z)=(2,1,1).     

Ihara's lemma for imaginary quadratic fields

An analogue over imaginary quadratic fields of a result in algebraic number theory known as Ihara's lemma is established. More precisely, we show that for a prime ideal p of the ring of integers of an imaginary quadratic field F, the kernel of the sum of the two standard p-degeneracy maps between the cuspidal sheaf cohomology is Eisenstein. Here Y₀ and Y₁ are analogues over F of the modular curves Y₀(N) and Y₀(Np), respectively. To prove our theorem we use the method of modular symbols and the congruence subgroup property for the group SL₂(Z[1/p]) which is due to Mennicke [J. Mennicke, On Ihara's modular group, Invent. Math. 4 (1967) 202-228] and Serre [J.-P. Serre, Le problème des groupes de congruence pour SL₂, Ann. of Math. (2) 92 (1970) 489-527].     

The distribution semantics for normal programs with function symbols

The distribution semantics integrates logic programming and probability theory using a possible worlds approach. Its intuitiveness and simplicity have made it the most widely used semantics for probabilistic logic programming, with successful applications in many domains. When the program has function symbols, the semantics was defined for special cases: either the program has to be definite or the queries must have a finite number of finite explanations. In this paper we show that it is possible to define the semantics for all programs. We also show that this definition coincides with that of Sato and Kameya on positive programs. Moreover, we highlight possible approaches for inference, both exact and approximate.     

A Laurent Expansion for Regularized Integrals of Holomorphic Symbols

For a holomorphic family of classical pseudodifferential operators on a closed manifold we give exact formulae for all coefficients in the Laurent expansion of its Kontsevich–Vishik canonical trace. This generalizes to all higher-order terms a known result identifying the residue trace with a pole of the canonical trace. Received: July 2005 Revision: December 2005 Accepted: January 2006     

LIE THEOREM VIA RANK 2 DISTRIBUTIONS (INTEGRATION OF PDE OF CLASS ω = 1)

In this paper we investigate compatible overdetermined systems of PDEs on the plane with one common characteristic. Lie's theorem states that its integration is equivalent to a system of ODEs, and we give a new proof by relating it to the geometry of rank 2 distributions. We find a criterion for integration in quadratures and in closed form, and discuss nonlinear Laplace transformations and symmetric PDE models.     

关于连续素数上取值的Legendre符号和的估计

利用Karatsuba的方法,研究了关于连续素数上取值的Legendre符号和∑p≤N(p q)的估计问题,得到了当q0.75+ω相似文献   

Berezin's quantization on flag manifolds and spherical modules

We show that the theory of spherical Harish-Chandra modules naturally gives rise to Berezin's symbol quantization on generalized flag manifolds. It provides constructions of symbol algebras and of their representations for covariant and contravariant symbols, and also for symbols which so far have no explicit definition. For all these symbol algebras we give a general proof of the correspondence principle.