[Csdmsemo] [math-ias] UPDATE: Topic and Abstract added to 5/17 Number Theory Seminar

[Kristina Phillips]

INSTITUTE FOR ADVANCED STUDY

School of Mathematics

Princeton, NJ 08540

 

Mathematics Seminars

Week of May 14, 2018

 

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Thursday, May 17
 
Joint IAS/Princeton University Number Theory Seminar
Topic:                     A new p-adic Maass-Shimura operator and
supersingular Rankin-Selberg p-adic L-functions
Speaker:                 Daniel Kriz, Princeton University
Time/Room:           4:30pm - 5:30pm/Fine Hall 214, Princeton University
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=137231

 

We introduce a new $p$-adic Maass-Shimura operator acting on a space of
"generalized $p$-adic modular forms" (extending Katz's notion of $p$-adic
modular forms) defined on the $p$-adic (preperfectoid) universal cover of
Shimura curves. Using this operator, we construct new $p$-adic $L$-functions
in the style of Katz, Bertolini-Darmon-Prasanna and Liu-Zhang-Zhang for
Rankin-Selberg families over imaginary quadratic fields $K$ in the case
where $p$ is inert or ramified in $K$. We also establish new $p$-adic
Waldspurger formulas, relating $p$-adic logarithms of elliptic units and
Heegner points to special values of these $p$-adic $L$-functions.

 

 

 

 

IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars

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