Two numbers are spectral equivalent if they have the same length spectrum. We show how to compute the equivalence classes of this relation. Moreover, we show that these classes can only have either 1, 2 or infinitely many elements.
We give a new proof of the fact that the vanishing of generalized Wronskians implies linear dependence of formal power series in several variables. Our results are also valid for quotients of germs of analytic functions.
Illinois at Urbana-Champaign for three years. He then moved to California and is now teaching at California State University, Dominguez Hills. His research interests are in model theory and number theory. While looking for exercises for a number theory class, I recently came across the following question in a book by André Weil [4, Question III.4]: Which… (More)