Number Theory study group: Around two problems of Hardy and Mahler
Let alpha and lambda be real numbers. About a century ago, Hardy asked: "In what circumstances can it be true that the distance of lambda alpha to the nearest integer tends to 0 as n goes to infinity?”. This question is still open. We will present some advances in this topic and around a related problem of Mahler, in the case alpha is algebraic. This is joint work with Purusottam Rath.