J. G. Webb, T. C. Ralph, and E. H. Huntington Centre for Quantum Computer Technology, School of Information Technology and Electrical Engineering, University College, The University of New South Wales, Canberra, Australian Capital Territory 2600, Australia Centre for Quantum Computer Technology, Department of Physics, The University of Queensland, St Lucia, Queensland 4072, Australia Received 1...

The probable behavior of am iuslance of size 1). of the stable marriage problem, chosen uniformly at rmdonl, is studied. Tl~e expected number of stable matchings is shown to be asymptotic t20 e-l77 In 1) for n m. The total rank of wonieu by nleu in the male optimal (pessimnl) matching is proven to be close to II In 11 (resp. T?.‘/ In j?), with high probability. 1980 Mat1~ema.tic.s Subject Class...

In this paper we study the sum , where denotes number of divisors n and { p } is a sequence integers indexed by primes. Under certain assumptions show that aforementioned . As an application, consider case given Fourier coefficients modular form.