7 citations · 18 across the 10 of their papers we have counts for
10 papers
A Proof of the Odd Perfect Number Conjecture
Simon Davis
It is sufficient to prove that there is an excess of prime factors in the product of repunits with odd prime bases defined by the sum of divisors of the integer $N=(4k+1)^{4m+1}\pr…
Effectively Closed Infinite-Genus Surfaces and the String Coupling
Simon Davis
The class of effectively closed infinite-genus surfaces, defining the completion of the domain of string perturbation theory, can be included in the category , which is charac…
A Rationality Condition for the Existence of Odd Perfect Numbers
Simon Davis
A rationality condition is derived for the existence of odd perfect numbers involving the square root of a product, which consists of a sequence of repunits, multiplied by twice th…
Spin Structures on Riemann Surfaces and the Perfect Numbers
Simon Davis
The equality between the number of odd spin structures on a Riemann surface of genus g, with being a Mersenne prime, and the even perfect numbers, is an indication that t…
Summability of Superstring Theory
Simon Davis
Several arguments are given for the summability of the superstring perturbation series. Whereas the Schottky group coordinatization of moduli space may be used to provide refined e…
Connections and Generalized Gauge Transformations
Simon Davis
Elimination of the fibre coordinate dependence from the connection form transformation rule for a bundle with a coset manifold standard fibre reduces the structure group. The nonli…