573 research outputs found
A study of the crank function in Ramanujan's Lost Notebook
In this note, we shall give a brief survey of the results that are found in
Ramanujan's Lost Notebook related to cranks. Recent work by B. C. Berndt, H. H.
Chan, S. H. Chan and W. -C. Liaw have shown conclusively that cranks was the
last mathematical object that Ramanujan studied. We shall closely follow the
work of Berndt, Chan, Chan and Liaw and give a brief description of their work.Comment: 12 pages, version 3, to appea
Some Smallest Parts Functions from Variations of Bailey's Lemma
We construct new smallest parts partition functions and smallest parts crank
functions by considering variations of Bailey's Lemma and conjugate Bailey
pairs. The functions we introduce satisfy simple linear congruences modulo
and . We introduce and give identities for two four variable
-hypergeometric functions; these functions specialize to some of our new
spt-crank-type functions as well as many known spt-crank-type functions
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