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BEGIN:VEVENT
UID:d330d004982db49abc51df779ea15995
CATEGORIES:Number Theory Seminar
CREATED:20210426T144943
SUMMARY:Arithmetic statistics of modular symbols
LOCATION:Zoom
DESCRIPTION:Abstract: The central value of the L-function of an elliptic curve has been
  the object of extensive studies in the last 50 years. Associated with such
  a curve we wish to understand also families of twists of it, leading to th
 e study of twisted L-functions. On the other hand modular symbols have been
  a useful tool to study the space of holomorphic cusp forms of weight 2, an
 d the homology of modular curves. They have been the object of extensive in
 vestigations by many mathematicians including Birch, Manin, and Cremona. Ma
 zur, Rubin, and Stein have recently formulated a series of conjectures abou
 t statistical properties of modular symbols in order to understand central 
 values of twists of elliptic curve L-functions. We discuss some of these co
 njectures and the recent progress and resolution of them. This is joint wor
 k with M. S. Risager.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="background: white;">Abstract:&nbsp;The central value of the L-fun
 ction of an elliptic curve has been the object of extensive studies in the 
 last 50 years. Associated with such a curve we wish to understand also fami
 lies of twists of it, leading to the study of twisted L-functions. On the o
 ther hand modular symbols have been a useful tool to study the space of hol
 omorphic cusp forms of weight 2, and the homology of modular curves. They h
 ave been the object of extensive investigations by many mathematicians incl
 uding Birch, Manin, and Cremona. Mazur, Rubin, and Stein have recently form
 ulated a series of conjectures about statistical properties of modular symb
 ols in order to understand central values of twists of elliptic curve L-fun
 ctions. We discuss some of these conjectures and the recent progress and re
 solution of them. This is joint work with M. S. Risager.</p>
CONTACT:Yiannis Petridis (University College London)
X-EXTRAINFO:https://rutgers.zoom.us/j/95892389306?pwd=WGZNamxBOXlGY1Y4RVpTOWthWlZVdz09\
 nZoom Password: rutgersnts\n
DTSTAMP:20260829T124405
DTSTART;TZID=America/New_York:20210427T140000
DTEND;TZID=America/New_York:20210427T150000
SEQUENCE:0
TRANSP:OPAQUE
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