We formulate, using heuristic reasoning, precise conjectures for the range of the number of primes in intervals of length yy around xx, where y≪(logx)^2y≪(logx)^2. In particular, we conjecture that the maximum grows surprisingly slowly as yy ranges from logxlogx to (logx)2(logx)^2. We will show that our conjectures are somewhat supported by available data, though not so well that there may not be room for some modification. This is joint work with Andrew Granville.
Additional Information
Allysa Lumley, Centre de Recherches Mathématiques, Montréal.
Please contact the organizers for Zoom meeting details here
Talks are usually at noon on Monday. All times are Mountain Time.