15 citations · 54 across the 29 of their papers we have counts for
34 papers
Patterns in the Markov numbers and their generalizations
Cormac O'Sullivan
Positive integer solutions to correspond to the important Markov (Markoff) numbers when . From a given solution triple, three more are found with Vieta…
Integer continued fractions for complex numbers
Cormac O'Sullivan
We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed…
Topographs for binary quadratic forms and class numbers
Cormac O'Sullivan
In this work we study, in greater detail than before, J.H. Conway's topographs for integral binary quadratic forms. These are trees in the plane with regions labeled by integers fo…
Integrality of the higher Rademacher symbols
Cormac O'Sullivan
Rademacher symbols may be defined in terms of Dedekind sums, and give the value at zero of the zeta function associated to a narrow ideal class of a real quadratic field. Duke exte…
Stirling's approximation and a hidden link between two of Ramanujan's approximations
Cormac O'Sullivan
A conjectured relation between Ramanujan's asymptotic approximations to the exponential function and the exponential integral is established. The proof involves Stirling numbers, s…
Ramanujan's approximation to the exponential function and generalizations
Cormac O'Sullivan
Ramanujan's approximation to the exponential function is reexamined with the help of Perron's saddle-point method. This allows for a wide generalization that includes the results o…