Threefield identities and simultaneous representations of primes by binary quadratic forms

JOURNAL OF NUMBER THEORY

卷:133

Article

Mortenson, Eric

关键词: Quadratic forms;    Hecke-type double sums;    Theta functions;   

DOI  :  10.1016/j.jnt.2013.05.001

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free