The Fischer-Griess monster group (M) and quadratic prime generating polynomials

Abstract

In this paper we show that, the quadratic prime-generating polynomials are connected to integer values of exactly 43 McKay- Thompson series of the conjugacy classes for the monster group. We have found that for p a prime divisor of |M|, Tp(t) is an algebraic number of degree one-half the h(-d). For p a product of two distinct prime divisors of |M|(except p=57 and p=93), the Tp(t) of the appropriate conjugscy class is an algebraic number of degree one-fourth the h(-d). For p a product of three distinct prime divisors of |M|, the Tp(t) of the appropriate conjugacy class is an algebraic number of degree one-eighth the h(-d).