REMINDER: Number Theory Seminars - Friday 24 October, 14:00 - 16:30 - Venue: ICTP Luigi Stasi Seminar Room (ERRATA CORRIGE)

[ICTP Math Section]

*_Number Theory Seminars_*

*_/PLEASE NOTE: THE CORRECT DATE IS FRIDAY, OCTOBER 24/_*

*VENUE:* ICTP Leonardo Building - Luigi Stasi Seminar Room

14:00 - 15:00 *Aleksander Simonič *(University of Primorska, Slovenia)

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

*Abstract:* Ingham (1940) proved that $N(\sigma,T)\ll 
T^{3(1-\sigma)/(2-\sigma)}\log^{5}{T}$, 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)


15:30 - 16:30 *Sumit Kumar* (Aarhus University, Denmark)

Title: *Second moment of GL(3) L-functions*

*Abstract:* Moments of L-functions play a fundamental role in number 
theory. In this talk we will estimate the second moment of L(1/2+it,F x 
chi), \chi a primitive character mod p^r and F a fixed GL(3) Hecke form 
averaged over t and chi. As an application we will obtain uniform 
subconvexity bounds for L(1/2+it, F x chi). This is ongoing joint work 
with Dasaratharaman, Leung and Pal.

All are welcome to attend

/https://indico.ictp.it/event/11206//
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Koutou Mabilo
ICTP Mathematics Group
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