Table of contents

This paper is a continuation of Part I (Math. USSR-Izv. 30 (1988), 15-38). Let  be a (semi) infinite nonselfintersecting continuous curve on a closed surface of nonpositive Euler characteristic and consider the behavior at "infinity" of the curve obtained by lifting  to the universal cover: either the Lobachevsky or the Euclidean plane. The possible types of this behavior for arbitrary  turn out to be the same as those for  which are semitrajectories of flows. Questions concerning the approach of to infinity along a definite direction are again considered. An example is constructed in which all points of the absolute are limit points in .

Bibliography: 12 titles.

Suppose ε > 0 is an arbitrarily small fixed number, Y ≥ Y₀(ε) > 0, and Consider the relationN₀(T + H) – N₀(T) ≥ cH ln T, where c = c(ε) > 0 is a constant depending only on ε, and let E denote the set of those T in the interval for which this relation does not hold. It is shown that the measure of this set satisfies

Bibliography: 19 titles.

Abelian torsion-free groups of finite rank with finite automorphism groups are considered as rigid extensions of a system of strongly indecomposable groups A_j, of finite rank and having finite automorphism groups, by a finite p-group P. Such groups are called -groups. The author introduces for -groups the concept of -type, which represents a choice of k integer matrices. A complete description of -groups is given by means of -types. Using this description, a series of problems on finite groups of automorphisms of torsion-free abelian groups of finite rank are solved. Furthermore, it is shown that the actual solution of any one of these problems comes down to a question of the consistency of a system of equations of the first degree modulo p^t, where p^t is the maximal order of elements of P.

Bibliography: 11 titles.

Let be an elliptic curve over , admitting a Weil parametrization , . Let be an imaginary quadratic extension of with discriminant , and let be a Heegner point. We show that if has infinite order ( must not belong to a finite set of fields that can be described in terms of ), then the Mordell-Weil group and the Tate-Shafarevich group of the curve (over ) are finite. For example, is finite. In particular, and are finite if and , where or is a rational prime such that and , where is the coefficient of in the -series of over . We indicate in terms of , , and a number annihilating and .

Bibliography: 11 titles.

The author presents a general method of reducing the study of various degenerate operators to that of model operators with quasihomogeneous symbols whose hypoellipticity conditions are formulated in terms of an auxiliary operator-valued symbol. A set of symbols is constructed whose invertibility implies hypoellipticity.

Bibliography: 13 titles.

This paper studies problems of the Dirichlet series expansions of elements of Smirnov spaces in convex domains, and related theorems on interpolation by entire functions of exponential type.

Bibliography: 22 titles.

A cut-elimination theorem for the second-order logic with an axiom of choice of type 0,1 or 1,1 is proved. In the first case the Päppinghaus scheme is applied; in the second the calculus with an epsilon-symbol for predicates is used.

Bibliography: 5 titles.

This paper studies irreducible representations of completely solvable finite-dimensional Lie algebras over an algebraically closed field of positive characteristic.

Bibliography: 12 titles.

Some uniqueness theorems for multiple trigonometric series are established, where the a_n are bounded and tend to zero, when all the coordinates of the vector n tend to infinity. Some boundary uniqueness properties for m-harmonic functions are also established.

Bibliography: 8 titles.

It is shown that local CR automorphisms of nondegenerate standard CR manifolds are rational and form a finite-dimensional Lie group. It is established that proper holomorphic mappings of nondegenerate Siegel domains are biholomorphic and rational.

Bibliography: 14 titles.

Let be an algebraic variety over an algebraically closed field , a sheaf on , and commutative Artinian -algebras, , where is a one-dimensional ideal, a deformation of with base , and the obstruction to the extension of the deformation to . The author constructs natural trace maps and proves that if is nonsingular then . As a consequence, a universal deformation of a simple sheaf on with nonsingular exists if the map is injective or, in the case , and , .

Bibliography: 3 titles.