University of Cambridge > Talks.cam > Combinatorics Seminar > Divisor distribution of random integers.

  Browse A-Z

Log in

University Account External (via Google)

🔐 Log In

Information on

Subscribing to talksdetails Finding a talkdetails Adding a talkdetails Disseminating talksdetails Help and Documentationdetails

ℹī¸ Information

Divisor distribution of random integers.

Download to your calendar using vCal

  • User Ben Green (Oxford)
  • ClockThursday 19 May 2022, 14:30-15:30
  • HouseMR12.

If you have a question about this talk, please contact HoD Secretary, DPMMS .

Let n be a random integer (sampled from {1,..,X} for some large X). It is a classical fact that, typically, n will have around (log n) divisors. Must some of these be close together? Hooley’s Delta function Delta(n) is the maximum, over all dyadic intervals I = [t,2t], of the number of divisors of n in I. I will report on joint work with Kevin Ford and Dimitris Koukoulopoulos where we conjecture that typically Delta(n) is about (log log n)c for some c = 0.353…. given by an equation involving an exotic recurrence relation, and then prove (in some sense) half of this conjecture, establishing that Delta(n) is at least this big almost surely. For the most part I will discuss a model combinatorial problem about representing integers in many ways as sums of elements from a random set.

This talk is part of the Combinatorics Seminar series.

This talk is included in these lists:

Note that ex-directory lists are not shown.

Other lists

OkayVBNG Boardroom, Department of Chemical Engineering HB101, Sir William Hardy Building Seminar Room.

Other talks

Title to be confirmed Using Light for Cancer Detection C2D3 Computational Biology Annual Symposium 2026 Dinner Title TBC Afternoon Break
 

Š 2006-2025 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity