Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Arvind Kumar
Affiliation:

The Hebrew University of Jerusalem
Date:

Wed, 26/01/2022 - 14:30 - 15:30 Determination of modular forms is one of the fundamental and interesting

problems in number theory. It is known that if the Hecke eigenvalues of two

newforms agree for all but finitely many primes, then both the forms are

the same. In other words, the set of Hecke eigenvalues at primes determine

the newform uniquely and this result is known as the multiplicity one

theorem. In the case of Siegel cuspidal eigenforms of degree two, the

multiplicity one theorem has been proved only recently in 2018 by Schmidt.

In this talk, we refine the result of Schmidt by showing that if the Hecke

eigenvalues of two Siegel eigenforms of level 1 agree at a set of primes of

positive density, then the eigenforms are the same (up to a constant). We

also distinguish Siegel eigenforms from the signs of their Hecke

eigenvalues. The main ingredient to prove these results are Galois

representations attached to Siegel eigenforms, the Chebotarev density

theorem and some analytic properties of associated L-functions.

For zoom details please contact Pieter Moree (moree@mpim-bonn.mpg.de [3])

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/246

[3] mailto:moree@mpim-bonn.mpg.de