Shinichi Kobayashi

collaborators

4 papers

math.NT2026

Anticyclotomic Iwasawa theory of CM elliptic curves at ramified primes

Ashay Burungale, Shinichi Kobayashi, Kentaro Nakamura +1

We propose an integral framework for the anticyclotomic Iwasawa theory of CM elliptic curves $E$ at primes $p$ ramified in the CM field. The $ε$ -constants of the geometri…

math.NT2025

Hecke $L$ -values, definite Shimura sets and Mod $ℓ$ non-vanishing

Ashay A. Burungale, Wei He, Shinichi Kobayashi +1

Let $I^»$ be a self-dual Hecke character over an imaginary quadratic field $K$ of infinity type $(1, 0)$ . Let $ℓ$ and $p$ be primes which are coprime to $6N_{K/\mathbb{Q}}({\mathr…

math.NT2025

A local sign decomposition for symplectic self-dual Galois representations of rank two

Ashay Burungale, Shinichi Kobayashi, Kentaro Nakamura +1

We prove the existence of a new structure on the first Galois cohomology of generic families of symplectic self-dual $p$ -adic representations of $G_{Q_{p}}$ of rank two (a l…

math.NT2025

The $p$ -adic valuation of local resolvents, generalized Gauss sums and anticyclotomic Hecke $L$ -values of imaginary quadratic fields at inert primes

Ashay Burungale, Shinichi Kobayashi, Kazuto Ota

We prove an asymptotic formula for the $p$ -adic valuation of Hecke $L$ -values of an imaginary quadratic field at an inert prime $p$ along the anticyclotomic $Z_{p}$ -tower. T…

Anticyclotomic Iwasawa theory of CM elliptic curves at ramified primes

Hecke L-values, definite Shimura sets and Mod ℓ non-vanishing

A local sign decomposition for symplectic self-dual Galois representations of rank two

The p-adic valuation of local resolvents, generalized Gauss sums and anticyclotomic Hecke L-values of imaginary quadratic fields at inert primes

Hecke $L$ -values, definite Shimura sets and Mod $ℓ$ non-vanishing

The $p$ -adic valuation of local resolvents, generalized Gauss sums and anticyclotomic Hecke $L$ -values of imaginary quadratic fields at inert primes