Aleksander Simonic: An explicit form of Ingham's zero density estimate

V torek, 7. oktobra ob 12. uri in 30 minut, bo v okviru seminarja za kompleksno analizo predaval dr. Aleksander Simonič z Univerze na Primorskem.

Title: An explicit form of Ingham's zero density estimate.

Abstract: Ingham (1940) proved that N(\sigma,T) << T^{3(1-\sigma)/(2-\sigma)} \log^5(T), where N(\sigma,T) counts the number of the non-trivial zeros \rho of the Riemann zeta-function with \Re(\rho) \geq \sigma \geq 1/2 and 0 < \Im(\rho) \leq T. Such estimates are often valuable in the distribution theory of prime numbers. In this talk I will present an explicit version of this result with the exponent (7-5\sigma)/(2-\sigma) of the logarithmic factor. The crucial ingredient in the proof is an explicit estimate with asymptotically correct main term for the fourth power moment of the Riemann zeta-function on the critical line, a result which is of independent interest. This is joint work with Shashi Chourasiya (UNSW Canberra).

Predavanje bo potekalo hibridno, v predavalnici 3.05 na Jadranski 21 in preko aplikacije ZOOM:

https://uni-lj-si.zoom.us/j/93433347588

Meeting ID: 934 3334 7588

Vljudno vabljeni!

Vodji seminarja

Franc Forstneric in Barbara Drinovec Drnovsek