Recent investigations of L-invariants of modular forms (John Bergdall, Bryn Mawr College / MPIM Bonn)

Séminaire « Arithmétique »
M2 Kampé de Fériet
This talks focuses on recent numerical investigations of L-invariants. Mazur, Tate, and Teitelbaum discovered L-invariants in the 1980's. They sought a p-adic analogue to Birch and Swinnerton-Dyer's conjecture on elliptic curves. In the decades since, L-invariants have arisen in many further arithmetic contexts. This includes: L-functions, families of modular forms, and Galois representations. Our talk highlights computations of L-invariants carried out in a range of contexts. We further raise distributional questions. These complement open questions about the non-Archimedean behavior of Hecke eigenvalues. Our contributions are part of an ongoing joint project with Robert Pollack.

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