Showing papers by "James Z. Wang published in 1994"

Analytic Number Theory, Complex Variable and Supercomputers

Abstract: This paper is the nal report of an undergraduate honors thesis project advised by Prof Dennis Hejhal of the School of Mathematics University of Minnesota The main pur pose of this project is to examine the analytic properties of certain quantum mechanical particles in Lobachevsky space The results were obtained on vectorized CRAY serial supercomputers a CRAY CPU T D massively parallel system and a K CPU mas sively parallel system CM located in University of Minnesota Using complex arithmetic we have successfully determined numerous Fourier coe cients for certain types of holo morphic modular forms including the Ramanujan function Our experiments involve both arithmetic and non arithmetic groups The treatment of the latter is new Analyzing the output data enables us to experimentally justify a number of properties Finally a veri cation of a Central Limit Theorem for automorphic functions on Hecke Groups was attempted and very promising results have been obtained Analytic Number Theory Complex Variable and Supercomputers