Discrepancy estimates for a class of normal numbers
Discrepancy estimates for some linear generalized monomials
We consider sequences modulo one that are generated using a generalized polynomial over the real numbers. Such polynomials may also involve the integer part operation [·] additionally to addition and multiplication. A well studied example is the (nα) sequence defined by the monomial αx. Their most basic sister, , is less investigated. So far only the uniform distribution modulo one of these sequences is resolved. Completely new, however, are the discrepancy results proved in this paper. We show...
Discrepancy estimates for the value-distribution of the Riemann zeta-function I
Discrepancy estimates for the value-distribution of the Riemann zeta-function III
Discrepancy of cartesian products of arithmetic progressions.
Discrepancy of normal numbers
Discrepancy of sums of three arithmetic progressions.
Discrepancy of symmetric products of hypergraphs.
Discrepancy of weighted matrix nets
Discrepancy Operators and Numerical Integration on Compact Groups.
Discrete analogues of singular and maximal Radon transforms.
Discrete and dense subgroup problems. (Problemas con subgrupos discretos y subgroupos densos.)
Discrete limit theorems for general Dirichlet series. III
Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given.
Discrete limit theorems for the Laplace transform of the Riemann zeta-function
In the paper discrete limit theorems in the sense of weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Laplace transform of the Riemann zeta-function are proved.
Discrete limit theorems for the Mellin transform of the Riemann zeta-function
Discrete planes, -actions, Jacobi-Perron algorithm and substitutions
We introduce two-dimensional substitutions generating two-dimensional sequences related to discrete approximations of irrational planes. These two-dimensional substitutions are produced by the classical Jacobi-Perron continued fraction algorithm, by the way of induction of a -action by rotations on the circle. This gives a new geometric interpretation of the Jacobi-Perron algorithm, as a map operating on the parameter space of -actions by rotations.
Discrete self-similar multifractals with examples from algebraic number theory
Discrete universality of the -functions of elliptic curves.
Discrete Value -- Distribution of L-functions of Elliptic Curves