3 papers
math.NT2025
The Rogers--Ramanujan continued fraction
Bruce C. Berndt, Örs Rebák
The primary purpose of this paper is to provide a survey of properties, values, identities, and generalizations of the Rogers--Ramanujan continued fraction, which is closely relate…
math.NT2024
Identities for the product of Two Dirichlet Series Satisfying Hecke's Functional Equation
Bruce C. Berndt, Likun Xie
We derive a general formula for the product of two Dirichlet series that satisfy Hecke's functional equation. Several examples are provided to demonstrate the applicability of the…
math.NT2024
Sums of two squares and the tau-function: Ramanujan's trail
Bruce C. Berndt, Pieter Moree
Ramanujan, in his famous first letter to Hardy, claimed a very precise estimate for the number of integers that can be written as a sum of two squares. Far less well-known is that…