## Arithmetic Randomness

### Project

The aim of the Austrian-French joint project ArithRand ("Arithmetic Randomness", 2021-2025) is to make progress on various questions that interrelate and link the notion of randomness (or pseudo-randomness) with the notion of determinism in the context of analytic number theory, combinatorics on words, automata theory, quasi-random sequences and nearby disciplines. It is financially supported by the FWF (Fonds zur Förderung der wissenschaftlichen Forschung, I 4945-N) and the ANR (Agence Nationale de la Recherche, ANR-20-CE91-0006).

### Research topics

Many numbertheoretic sequences are per se deterministic but resemble much of the overall behaviour of a random sequence. One important example is the Möbius function. In this context we are interested in studying the independence between the Möbius function and various deterministic functions such as functions that are produced by a dynamical system of zero entropy or by a simple algorithm based on the binary digital representation. Informally, the difficulty of this independence problem reflects the difficulty of the transition from the digital representation of an integer to its multiplicative representation as a product of prime factors. This field of questions is the source of many important open problems in mathematics and computer science. In particular, we mention the construction of normal numbers, the analysis of pseudo-random and complexity measures, and the search for optimal discrepancy estimates for digitally based sequences or other quasi-random sequences which are some of the major lines of research in this joint project.

### Members

The Austrian-French Consortium consists of 16 researchers and is based in Graz, Vienna, Bordeaux, Calais, Marseille, Nancy and St Etienne.

- Aistleitner Christoph (Technische Universität Graz)
- Dartyge Cécile (Université de Lorraine)
- Deshouillers Jean-Marc (Institut polytechnique de Bordeaux)
- Drappeau Sary (Université d'Aix-Marseille)
- Drmota Michael (Technische Universität Wien)
- Elsholtz Christian (Technische Universität Graz, Austrian Coordinator)
- Grabner Peter (Technische Universität Graz)
- Martin Bruno (Université du Littoral)
- Müllner, Clemens (Technische Universität Wien)
- Ramaré Olivier (Université d'Aix-Marseille)
- Rivat Joël (Université d'Aix-Marseille)
- Robert Olivier (Université Jean Monnet, Lyon, St Etienne)
- Spiegelhofer Lukas (Technische Universität Wien)
- Stoll Thomas (Université de Lorraine, French coordinator)
- Tenenbaum Gérald (Université de Lorraine)
- Tichy Robert (Technische Universität Graz)

Postdoctoral researchers:

- to come

Doctoral students:

- to come

### Events

- to come

### Guests (selection)

- to come

### Publications/Preprints / in preparation (explicitely mentioning ArithRand)

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### Talks

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