Self-avoiding walks on the simple cubic lattice

We have substantially extended the series for the number of self-avoiding w alks and the mean-square end-to-end distance on the simple cubic lattice. O ur analysis of the series gives refined estimates for the critical point an d critical exponents. Our estimates of the exponents gamma and nu are in go od agreement with recent high-precision Monte Carlo estimates, and also wit h recent renormalization group estimates. Critical amplitude estimates are also given. A new, improved rigorous upper bound for the connective constan t mu < 4.7114 is obtained.