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SUMMARY:Mahler Measures and Dirichlet L-Functions: New Results on Chinburg
 ’s Conjectures [MPIM]
DTSTART:20260429T123000Z
DTEND:20260429T133000Z
DTSTAMP:20260508T062600Z
UID:indico-event-1266@math-events.uni-bonn.de
DESCRIPTION:Speakers: Mahya Mehrabdollahi (MPIM)\n\nNumber theory lunch se
 minar\nThis talk concerns Chinburg’s conjectures\, which propose a conne
 ctionbetween two a priori different objects: Mahler measures and certain s
 pecialvalues of Dirichlet L-functions associated with odd quadratic charac
 ters.\nThe Mahler measure of a polynomial is the arithmetic mean of log|P|
  overthe unit torus. Chinburg’s conjecture (1984) states that\, for each
  oddquadratic Dirichlet character\, there exists an integral bivariate rat
 ionalfunction (or\, in its strongest form\, an integral polynomial) whose 
 Mahlermeasure is equal to a rational multiple of the derivative at −1 of
  thecorresponding L-function. This relationship is currently known only in
  alimited number of cases (18 values of the conductor of the Dirichletchar
 acter).\nI will present recent results obtained in collaboration with Davi
 d Hokkenand Berend Ringeling\, in which we construct new examples for prev
 iouslyunknown conductors\, thereby doubling the number of verified cases. 
 Finally\,we establish a special case of the conjecture when coefficients i
 n acyclotomic extension are allowed.\n\nhttps://math-events.uni-bonn.de/ev
 ent/1266/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1266/
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