Monday, April 27, 2015

"On Liouville's Function" by Lehman, 1960

I calculate some of the results in the paper On Liouville's Function, R. Sherman Lehman, Math. Comp. 14 (1960), 311-320 with Mathematica. I find this paper interesting because it is an old paper that used a computer to find an explicit counterexample to a conjecture of Polya. I also find it interesting because thinking about how to compute number theoretic functions helps to understand the formulas better. The names of the sections below are the same as in the paper. Equation numbers refer to the equations in the paper.