BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Siddhi Pathak (Pennsylvania State University)
DTSTART:20200529T123000Z
DTEND:20200529T133000Z
DTSTAMP:20260513T213325Z
UID:CMI/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CMI/9/">Arit
 hmetic nature of special values of L-functions</a>\nby Siddhi Pathak (Penn
 sylvania State University) as part of CMI seminar series\n\n\nAbstract\nTh
 e study of L-functions has occupied a center stage in number theory since 
 the work of Riemann and Dirichlet. A standard example of an L-function is 
 the Riemann zeta-function\, $\\zeta(s)$\,  given by the series $\\sum_{n=1
 }^{\\infty} n^{-s}$ when $\\Re(s)>1$. The aim of this talk will be to disc
 uss the question of determining the arithmetic nature (that is\, rational/
 irrational and algebraic/transcendental) of values of L-functions at posit
 ive integers. For example\, it is expected that the values $\\zeta(m)$ are
  transcendental for all integers $m >1$. However\, the only known cases of
  this conjecture are the even zeta-values\, which Euler had explicitly eva
 luated in the 1730s. Among the odd zeta-values\, Apery proved that $\\zeta
 (3)$ is irrational\, whereas the irrationality of the remaining odd zeta-v
 alues remains a mystery. \n\nIn this talk\, we will discuss various facets
  of this problem. If time permits\, we will prove that for a fixed odd pos
 itive integer m\, all the values $\\zeta_K(m)$ are irrational as K varies 
 over imaginary quadratic fields\, with at most one possible exception. Thi
 s is joint work with Ram Murty. This talk will be accessible to a wide aud
 ience.\n
LOCATION:https://researchseminars.org/talk/CMI/9/
END:VEVENT
END:VCALENDAR