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SUMMARY:Kwun Angus Chung (University of Michigan)
DTSTART:20210121T220000Z
DTEND:20210121T230000Z
DTSTAMP:20260423T024724Z
UID:UCSD_NTS/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/24/
 ">$v$-adic convergence for exp and log in function fields and applications
  to $v$-adic $L$-values</a>\nby Kwun Angus Chung (University of Michigan) 
 as part of UCSD number theory seminar\n\nLecture held in normally APM 7321
 \, currently online.\n\nAbstract\nClassically over the rational numbers\, 
 the exponential and logarithm series converge $p$-adically within some ope
 n disc of $\\mathbb{C}_p$. For function fields\, exponential and logarithm
  series arise naturally from Drinfeld modules\, which are objects construc
 ted by Drinfeld in his thesis to prove the Langlands conjecture for $\\mat
 hrm{GL}_2$ over function fields. For a "finite place" $v$ on such a curve\
 , one can ask if the exp and log possess similar $v$-adic convergence prop
 erties. For the most basic case\, namely that of the Carlitz module over $
 \\mathbb{F}_q[T]$\, this question has been long understood. In this talk\,
  we will show the $v$-adic convergence for Drinfeld-(Hayes) modules on ell
 iptic curves and a certain class of hyperelliptic curves. As an applicatio
 n\, we are then able to obtain a formula for the $v$-adic $L$-value $L_v(1
 \,\\Psi)$ for characters in these cases\, analogous to Leopoldt's formula 
 in the number field case.\n\npre-talk\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/24/
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