Charles Sims has asked whether or not, for a free group F , the lower central subgroup γn(F ) coincides with the normal closure in F of the set of basic commutators of weight n. In this paper, we will show that Sims’ question has a positive answer when n = 5. The longest part of the proof is showing that this is true when F has rank 3. Once this is known, the results for higher ranks follow fai...

In this article, we study the Mertens conjecture. We revisit and improve the original constructive disproof of János Pintz. We obtain a new lower bound for the minimal counterexample and new numerical results for this conjecture.

Mathematical FinanceVolume 33, Issue 1 p. 16-18 OBITUARY Marco Avellaneda: Mathematician and trader Jim Gatheral, Corresponding Author Gatheral [email protected] orcid.org/0000-0002-0192-8797 Department of Mathematics, Baruch College, New York, USA Correspondence Mathematics Box B6-230, College One Bernard Way NY 10010, USA. Email: protected]Search for more papers by this author First published...