For Rankin-Selberg products of Hida and Coleman families, the paper proves equality of characteristic ideals of Selmer groups under the involution, yielding functional equations for algebraic p-adic L-functions.
Factorization of Algebraic $p$-adic $L$-functions Attached to Adjoint Representations of Coleman Families: Non-critical Case
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abstract
The main objective of this article is to establish the $p$-adic Artin formalism for the algebraic $p$-adic $L$-functions attached to the adjoint representations of Coleman families of modular forms. In particular, we prove a factorization formula involving the determinants of appropriate Selmer complexes, using tools from rigid geometry, homological algebra, Euler systems, and $p$-adic Hodge theory. This work extends an earlier result of Palvannan to the $p$-non-ordinary setting.
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Functional equations of algebraic Rankin-Selberg $p$-adic $L$-functions
For Rankin-Selberg products of Hida and Coleman families, the paper proves equality of characteristic ideals of Selmer groups under the involution, yielding functional equations for algebraic p-adic L-functions.