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SUMMARY:Ming-Lun Hsieh (Academia Sinica)
DTSTART:20211105T143000Z
DTEND:20211105T160000Z
DTSTAMP:20260423T024446Z
UID:CAFAS/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAFAS/30/">O
 n the first derivatives of the cyclotomic Katz p-adic L-functions for CM f
 ields</a>\nby Ming-Lun Hsieh (Academia Sinica) as part of Columbia Automor
 phic Forms and Arithmetic Seminar\n\n\nAbstract\nBuyukboduk and Sakamoto i
 n 2019 proposed a precise conjectural formula relating the leading coeffic
 ient at the trivial zero s=0 of the cyclotomic Katz p-adic L-functions ass
 ociated with ray class characters of a CM field K to suitable L-invariants
 /regulators of K. They were able to prove this formula in most cases when 
 K is an imaginary quadratic field thanks to the existence of the Euler sys
 tem of elliptic units/Rubin-Stark elements. In this talk\, we will present
  a formula relating the first derivative of the cyclotomic Katz p-adic L-f
 unctions for general CM fields attached to ring class characters to the pr
 oduct of the L-invariant and the value of the improved Katz p-adic L-funct
 ion at s=0. In particular\, when the trivial zero occurs at s=0\, we prove
  that the Katz p-adic L-function has a simple zero at s=0 if certain L-inv
 ariant is non-vanishing. Our method uses the congruence of Hilbert CM form
 s and does reply on the existence of the conjectural Rubin-Stark elements.
  This is a joint work with Adel Betina.\n
LOCATION:https://researchseminars.org/talk/CAFAS/30/
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