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SUMMARY:Largest prime factor of n^2+1
DTSTART:20191126T151500
DTEND:20191126T161500
DTSTAMP:20260415T075800Z
UID:5c91466721bef05c075bdde7aabe35208b6534539de86a94d812cac1
CATEGORIES:Conferences - Seminars
DESCRIPTION:Jori Merikoski (Turku)\nA famous open problem in number theory
  is to show that there are infinitely many prime numbers of the form n^2+1
 . To approach this we may consider the largest prime factor of n^2+1. In t
 his talk I will show that the largest prime factor of n^2+1 is infinitely 
 often greater than n^{1.279}. This improves the result of de la Bretèche 
 and Drappeau who obtained this with the exponent 1.2182 in place of 1.279.
  The main new ingredients in the proof are the use Harman's sieve method a
 nd a new bilinear estimate which is proved by applying the Deshouillers-Iw
 aniec bounds for sums of Kloosterman sums. Assuming Selberg's eigenvalue c
 onjecture I show that the exponent 1.279 can be increased to 1.312.
LOCATION:GR A3 30 https://plan.epfl.ch/?room==GR%20A3%2030
STATUS:CONFIRMED
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