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SUMMARY:On the average of class numbers of real quadratic fields [MPIM]
DTSTART:20260909T123000Z
DTEND:20260909T133000Z
DTSTAMP:20260903T152200Z
UID:indico-event-1558@math-events.uni-bonn.de
DESCRIPTION:Speakers: Yijie Diao (ISTA)\n\nPLeaSANT\nThe average behaviour
  of class numbers of real quadratic fields is still poorly understood. Let
  $S(X)$ denote the sum of the class numbers of real quadratic fields with 
 discriminant at most $X$. The class number formula gives the elementary bo
 und $S(X)\\ll X^{3/2}$\, while a classical result of Siegel gives the best
  known upper bound $S(X)\\ll X^{3/2}/\\log X$. On the other hand\, Hooley 
 conjectured that $S(X)$ should be of order $X(\\log X)^2$. There is theref
 ore a substantial gap between what is known and what is expected. In this 
 talk\, I will discuss this problem and some recent progress on it.\n\nhttp
 s://math-events.uni-bonn.de/event/1558/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1558/
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