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January 20 Math Colloquium

Paul Young, CofC

Relations among p-adic zeta functions

In this talk, I will focus on two unusual new theorems. The first is a surprising and powerful system of congruences for sums involving Fibonacci and Lucas numbers and Bernoulli numbers. The second result is concerned with a family of hypergeometric series which are related to PI, and I will show how to make some of the PI disappear.

These two eccentric and esoteric results were derived from functional equations for p-adic zeta functions, which I developed during my recent sabbatical leave. After showing how to get these theorems, I’ll explain the more general results one can get from this theory. I will conclude with some examples showing how all this p-adic nonsense can tell us something about REAL things.

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