Matrices with multiplicative entries
Heilbronn Number Theory Seminar
17th January 2018, 4:00 pm – 5:00 pm
Howard House, 4th Floor Seminar Room
We study matrices (both finite and infinite) whose entries are a multiplicative function of two variables. We show that the operators represented by such matrices are infinite tensor products over the primes, like an Euler product. Applications to finding the eigenvalues explicitly of arithmetical matrices are given; also Multiplicative Toeplitz and Hankel operators whose entries are of the form f(i/j) and g(ij) respectively are discussed.