Randomized trial shows the geometric construction of p-adic L-values in quadratic extensions, indicating novel insights for number theory.
Key Points
The study aims to explore the relationship between Hirzebruch-Zagier cycles and p-adic adjoint L-values in quadratic extensions of totally real number fields.
Demonstrated the existence of generalized Hirzebruch-Zagier cycles in p-adic families derived from Hilbert modular varieties.
Utilized base change theory to connect geometric constructions with multivariable p-adic adjoint L-functions.
Examined Hida families of Hilbert modular forms associated with the quadratic extension.
Generalized Hirzebruch-Zagier cycles can be embedded in p-adic families, expanding their applications in number theory.
Provided a geometric approach to constructing the multivariable p-adic adjoint L-function linked to the Hecke character of E/F.