Alladi Ramakrishnan Hall

On some problems in Matsuda monoids

Sunil Naik

Queens University

Let F be a field and M be commutative, torsion-free, cancellative monoid. Let F[X; M] denote the ring of all polynomials with coefficients in F and exponents in M. We say that M is a Matsuda monoid if for every indivisible element $\alpha$ in M, the polynomial $X^{\alpha} - 1$ is irreducible in F[X; M] for any field F. In this talk, we will discuss recent work on Matsuda monoids that leads to questions in analytic number theory.