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CATEGORIES:Combinatorics Seminar
SUMMARY:Divisor distribution of random integers. -  Ben Gr
 een (Oxford)
DTSTART;TZID=Europe/London:20220519T143000
DTEND;TZID=Europe/London:20220519T153000
UID:TALK173945AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/173945
DESCRIPTION: Let n be a random integer (sampled from {1\,..\,X
 } for some large\nX). It is a classical fact that\
 , typically\, n will have around (log n)^{log\n2} 
 divisors. Must some of these be close together? Ho
 oley's Delta function\nDelta(n) is the maximum\, o
 ver all dyadic intervals I = [t\,2t]\, of the\nnum
 ber of divisors of n in I. I will report on joint 
 work with Kevin Ford\nand Dimitris Koukoulopoulos 
 where we conjecture that typically Delta(n) is\nab
 out (log log n)^c for some c = 0.353.... given by 
 an equation involving\nan exotic recurrence relati
 on\, and then prove (in some sense) half of this\n
 conjecture\, establishing that Delta(n) is at leas
 t this big almost surely.\nFor the most part I wil
 l discuss a model combinatorial problem about\nrep
 resenting integers in many ways as sums of element
 s from a random set.
LOCATION:MR12
CONTACT:HoD Secretary\, DPMMS
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