What is a Gauss factorial?
- Dr John B Cosgrave (formerly St Patrick's College, Dublin)
- 13 October 2010
- 2:00 pm - Location G.107
A Gauss factorial is an entirely new object in Number Theory and this colloquium talk, which is aimed at a non-specialist audience with no previous knowledge of Number Theory, will describe it and the context in which it arises.
Gauss' generalisation of Wilson's theorem was given in his renowned classic, the Disquisitiones Arithmeticae (1801). In 2008, Karl Dilcher and I gave the first extension of the Gauss-Wilson theorem, the key new object being what we call a 'Gauss factorial'. This entirely elementary object opens up a whole new world of interest, revealing many new results in Number Theory, especially in connection with classic, beautiful binomial coefficient congruences of Gauss and Jacobi.