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SUMMARY:Igor Shparlinski (The University of New South Wales\, Sydney\, Aus
 tralia)
DTSTART:20200731T110000Z
DTEND:20200731T120000Z
DTSTAMP:20260423T021352Z
UID:NTdL/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTdL/14/">In
 tegers of prescribed arithmetic structure in residue classes</a>\nby Igor 
 Shparlinski (The University of New South Wales\, Sydney\, Australia) as pa
 rt of Number theory during lockdown\n\n\nAbstract\nWe give an overview of 
 recent results about the distribution of some special integers in residues
  classes modulo a large integer $q$. Questions of this type were introduce
 d by Erdos\, Odlyzko and Sarkozy (1987)\, who considered products of two p
 rimes as a relaxation of the classical question about the distribution of 
 primes in residue classes. Since that time\, numerous variations have appe
 ared for different sequences of integers. The types of numbers we discuss 
 include smooth\, square-free\, square-full and almost primes integers. We 
 also expose\, without going into technical details\, the wealth of differe
 nt techniques behind these results: sieve methods\, bounds of short Kloost
 erman sums\, bounds of short character sums and many others.\n
LOCATION:https://researchseminars.org/talk/NTdL/14/
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