We prove that for every c < 1 there exists arbitrarily large T with
|ζ(1/2+iT )| > exp(c sqrt(logT logloglogT / loglogT)).
This improves classical results by Montgomery, Balasubramanian-Ramachandra, and Soundararajan. We will discuss the main components of the proof: Soundararajan’s resonance method, multiplicative functions, and convolution formulas for the Riemann zeta function. Further applications of the suggested approach will be considered.
Extreme values of the Riemann zeta function and its argument
29.10.2019 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: