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4 papers · 2 filters
The Landau function and the Riemann Hypothesis
Marc Deleglise, Jean-Louis Nicolas
The Landau function is the maximal order of an element of the symmetric group of degree ; it is also the largest product of powers of primes whose sum is . The mai…
A note on Christol's theorem
Boris Adamczewski, Reem Yassawi
Christol's theorem characterises algebraic power series over finite fields in terms of finite automata. In a recent article, Bridy develops a new proof of Christol's theorem by Spe…
On the density or measure of sets and their sumsets in the integers or the circle
Pierre-Yves Bienvenu, François Hennecart
Let be the asymptotic density (if it exists) of a sequence of integers . For any real numbers , we solve the question of the existence of a se…
An extension of Macdonald's identity for
Quentin Gazda
Let be an odd positive integer. In this short elementary note, we slightly extend Macdonald's identity for into a two-variables identity in the spirit of Ja…