arXiv subjects

Eric T. Mortenson

Publications and source records attributed to Eric T. Mortenson.

21 records · Page 2Linked to original sources

arXiv2017

A Kronecker-type identity and the representations of a number as a sum of three squares

By considering a limiting case of a Kronecker-type identity, we obtain an identity found by both Andrews and Crandall. We then use the Andrews-Crandall identity to give a new proof of a formula of Gauss for the representations of a number as a sum of three squares. From the Kronecker-type identity, we also deduce Gauss's theorem that every positive integer is representable as a sum of three triangular numbers.

math.NT↗

arXiv2016

On the tenth-order mock theta functions

Using properties of Appell-Lerch functions, we give insightful proofs for six of Ramanujan's identities for the tenth-order mock theta functions.

math.NT↗

arXiv2016

A double-sum Kronecker-type identity

We prove a double-sum analog of an identity known to Kronecker and then express it in terms of functions studied by Appell and Kronecker's student Lerch, in so doing we show that the double-sum analog is of mixed mock modular form. We also give related symmetric generalizations.

math.NT↗