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DTSTART;TZID=America/Toronto:20251007T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-150
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:ALEX COWAN\, UNIVERSITY OF WATERLOO\n\n_Murmurations from funct
 ional equations_\n\nUnexpected and striking oscillations in the average a_
 p values of sets\nof elliptic curves\, dubbed murmurations\, were recently
  discovered\nusing techniques from data science. Since then\, similar patt
 erns have\nbeen discovered for many other types of arithmetic objects. In 
 this\ntalk we present a new approach for studying murmurations\, revolving
 \naround mean values of L-functions in the critical strip and guided by\nr
 andom matrix theory. With our approach\, we prove murmurations in many\nca
 ses conditional on standard conjectures\, and unconditionally for all\nGL_
 1 automorphic representations. To handle the case of elliptic\ncurves know
 ledge is needed of the distribution of conductors of\nelliptic curves when
  ordered by height\, which is of independent\ninterest.\n\nMC 5417
DTSTAMP:20260407T174925Z
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