The work of Matomaki and Radziwill on average value of the \lambda function
Event details
| Date | 01.10.2015 |
| Hour | 14:15 › 15:15 |
| Speaker | Harald Helfgott - Georg-August-Universität Göttingen |
| Location | |
| Category | Conferences - Seminars |
Let f be a multiplicative function. Let $h = h(x)\to infty$ (arbitrarily slowly) when $x\to \infty$. Kaisa Matomaki and Maksym Radziwill have proved that, for a proportion tending to 1 of all X\leq x\leq 2X, the average of f(n) from x to x+h is within o(1) of the average of f(n) from x to 2x.
This result - whose proof is remarkably elegant and straightforward - is much stronger than what was known before, even for specific multiplicative functions. For example, for f = mu or f = lambda (the Moebius and Louiville functions), we had such results only for h>=x^(1/6).
There have already been applications towards Chowla's conjecture (in part by Matomaki-Radziwill and in part by Tao, or both). We will go over the proof for f = lambda.
The talk is meant to be an incentive to a discussion in depth of these recent results.
This result - whose proof is remarkably elegant and straightforward - is much stronger than what was known before, even for specific multiplicative functions. For example, for f = mu or f = lambda (the Moebius and Louiville functions), we had such results only for h>=x^(1/6).
There have already been applications towards Chowla's conjecture (in part by Matomaki-Radziwill and in part by Tao, or both). We will go over the proof for f = lambda.
The talk is meant to be an incentive to a discussion in depth of these recent results.
Practical information
- General public
- Free
Organizer
- TAN
Contact
- Monique Kiener