Gál type GCD sums and extreme values of the Riemann zeta function

Add to your list(s) Download to your calendar using vCal

• Kristian Seip (NTNU)
• Tuesday 01 March 2016, 14:15-15:15
• MR13, Centre for Mathematical Sciences.

If you have a question about this talk, please contact Jack Thorne.

In recent joint work with Aistleitner, Berkes, Bondarenko, and Hilberdink, we have found optimal bounds for sums over k and l from 1 to N of gcd(nk,nl)^2S / (nk nl)^S where n1,..., nN are distinct positive integers and 0 < S < 1 . Such sums are named after Gál who in 1949, solving a prize problem proposed by Erdos, settled the case S=1. I will discuss the relation between such estimates and extreme values of |zeta(S+it)|. In particular, I will present the following theorem of Bondarenko and myself: For every c with 0 < c < 1/sqrt{2} there exists a B with 0 < B < 1 such that the maximum of |zeta(1/2+it)| for t between T to the B and T exceeds exp(c sqrt{log T logloglog T/ loglog T}) for all T large enough. Our proof relies on Soundararajan’s resonance method. I will outline the main novelties of our adaption of this method, including our usage of large Gál type sums.

This talk is part of the Number Theory Seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR13, Centre for Mathematical Sciences
• Number Theory Seminar
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.