Évènement

The objective of the present project is to connect uniform distribution theory with pseudorandomness as well as partitions. Let us first briefly describe the three areas.
Uniform distribution theory investigates the distribution of sequences in the unit interval. In particular we call a sequence uniformly distributed if for each interval the frequency of elements of the sequence lying in this interval asymptotically tends to the size of the interval. Otherwise said there is no area (interval) that is hit more or less often than the average.
Pseudorandomness provides tools in order to measure how random a given binary sequence behaves. Two main tools consider the distribution along arithmetic progressions as well as the correlation with a given shift vector. If both are small, then we suppose that the sequence behaves randomly.
Partitions of an integer are representations of this integer as sum of integers from a given infinite set. In this area one is interested in the length (number of summands) of a partition, the average size of a summand, the largest or the smallest summand on average etc.
The measures and methods that are introduced in order to describe the pseudorandom behaviour of a sequence have their counterparts in uniform distribution theory. In the present project we want to enlighten this link and to use it for transferring other concepts.
In order to obtain an asymptotic formula for the number of partitions we need that the infinite set does not prefer certain residue classes or other additive structures. This seems equivalent to showing that a certain connected sequence is indeed uniformly distributed. In the present project we want to generalise this connection in order to obtain results for arbitrary infinite sets.
Finally we want to use the connections between uniform distribution and pseudorandomness as well as partitions to generalise known results to subsequences such as the primes or square-free numbers.