Mathematics Seminar at ICTP - Wednesday 12 June at 14:00 (Micah MILINOVICH)

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S  2019


Wednesday 12 June, at 14:00 hrs.


Micah Milinovich (University of Mississippi - USA)


Title: The distribution of the zeros of the Riemann zeta-function


Abstract: It has long been known that the distribution of the prime 
numbers is intimately connected to the distribution of the zeros of the 
Riemann zeta-function. Much information can be obtained from the 
horizontal distribution of zeros, but finer information about primes 
seems to be connected to the vertical distribution of zeros.  By 
studying the pair correlation of the normalized spacing between the 
zeros, Montgomery was lead to the conjecture that the statistics of 
vertical spacings should follow the GUE distribution from random matrix 
theory. I will survey some of the methods used to prove the existence of 
large and small gaps between zeros of the zeta function, highlighting 
the state-of-the-art and the limitations. I will also discuss some 
recent joint work (with Hung Bui and Dan Goldston) were we prove the 
existence of small gaps between distinct zeros of the zeta function, a 
result that previous methods seem incapable of establishing.


http://indico.ictp.it/event/8973/


VENUE:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

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