Algebra and Number Theory Seminar: Mihir Deo

Title: 𝑝-adic Asai 𝐿-functions of Bianchi modular forms at non-ordinary primes

Abstract: For a prime 𝑝, one can view 𝑝-adic 𝐿-functions as power series with coefficients in a local field or in the ring of integers of a local field. These functions satisfy certain growth properties and interpolate special values of complex 𝐿-functions. In this talk, I will present the construction of 𝑝-adic Asai 𝐿-functions with unbounded coefficients attached to cuspidal Bianchi modular forms at non-ordinary primes. I will then discuss the Pollack, Sprung, and Lei—Loeffler--Zerbes style decomposition of these 𝑝-adic Asai 𝐿-functions with unbounded coefficients into signed 𝑝-adic Asai 𝐿-functions with bounded coefficients. The talk will begin with a brief review of 𝑝-adic 𝐿-functions, Bianchi modular forms, and their Asai 𝐿-functions.