RISC Forum
Ralf Hemmecke: Dancing Samba with Ramanujan Partition Congruences
| When |
Mar 13, 2017
from 01:30 PM to 01:45 PM |
|---|---|
| Where | RISC seminar room |
| Attendees |
all@risc |
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Ramanujan gave explicit formulas that show that for every natural number n it holds 5 | p(5n+4) and 7 | p(7n+5) where p(n) denotes the number of partitions of n. It is also known that p(11n+6) is divisible by 11. For the case 5 and 7 simple identities are know that show divisibility explicitly. We consider the case of divisibility of p(11n+6) by 11 and show what is already known and how we improve the situation. Our identity is given in terms of Dedekind $\eta$-functions and is obtained automatically from a modification of an algorithm by Radu.
In this talk we focus on the ideas that led to the above result.