Wednesday, October 11, 2017 - 11:30am
1 hour (actually 50 minutes)
Lunch will be provided. The talk will be the first 25 minutes of the hour and then will be followed by discussion.
In a recent article to appear in the American Mathematical Mothly next year, we use the Lambert series generating function for Euler’s totient function to introduce a new identity for the number of 1’s in the partitions of n. New expansions for Euler’s partition function p(n) are derived in this context. These surprising new results connect the famous classical totient function from multiplicative number theory to the additive theory of partitions. We will define partitions and several variants of Euler's partition function in the talk to state our new results.