CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Eventssee all events
Events        
next up previous
Next: Drew Vandeth - Transcendence Up: Graduate Student Seminar / Previous: Gregory S. Smith -

Sarah Sumner - Investigating transcendence in the field of p-adic numbers



SARAH SUMNER, Department of Mathematics and Statistics, Queen's University, Kingston, Ontario  K7L 3N6, Canada
Investigating transcendence in the field of p-adic numbers


In the field of p-adic numbers, whether the number $\sum_{n=1}^{\infty}\, n!$ is transcendental or even irrational is an unsolved problem. However, it can be shown that numbers of the form $\sum_{n=1}^{\infty} n^k \cdot n!$ can be written in the form $v_k -
u_k\sum_{n=1}^{\infty}\,n!$ where uk and vk are integers. Interesting congruences involving the series $\{u_k\}$ are developed and conditions that will produce a p-adic transcendental number are discussed.

This is joint work with Professor Ram Murty.



 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/