Kaplansky [2003] proved a theorem on the simultaneous representation of a prime p by two different principal binary quadratic forms. Later, Brink found five more like theorems and claimed that there were no others. By putting Kaplansky-like theorems into the context of threefield identities after Andrews, Dyson, and Hickerson, we find that there are at least two similar results not on Brink's list. We also show how such theorems are related to results of Muskat on binary quadratic forms. © 2013 Elsevier Inc.
Original languageEnglish
Pages (from-to)3902-3920
Number of pages19
JournalJournal of Number Theory
Volume133
Issue number11
DOIs
StatePublished - 1 Nov 2013

    Research areas

  • Hecke-type double sums, Quadratic forms, Theta functions

ID: 126317712