A Property of the Rayleigh Function

A Combinatorial Problem and Congruences for the Rayleigh Function

“…The main purpose of this paper is to consider the problem of evaluating/(z, s) for s è 0 and to show how this function can be used for proving congruences for the Rayleigh function, <r2n(v). We note that in [2] it was proved that/(z, 0) = 2m~1 -1.…”

“…Let a/b be a rational number, a odd, b even, b = (2k + l)2', and let y = 2« +1 + (1 -2n)t-m, where m is the number of nonzero terms in the base 2 expansion of 2«. In [2] the following results were proved. We can now prove the following theorems.…”