Arithmetic of Critical 𝑝-Adic 𝐿-Functions

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The research aims to develop a complete arithmetic theory of critical p-adic L-functions on the eigencurve.
Developed an étale construction of p-adic L-functions at a critical point on the eigen curve.
Introduced algebraic counterparts via Selmer complexes and developed Iwasawa theory.
Formulated critical main conjectures and established descent theory.
Formulated an infinitesimal thickening of the Iwasawa main conjecture, suggesting its strength over existing conjectures.
Established a leading term formula for p-adic L-functions over two-variable settings, enhancing understanding of p-adic constructions.

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This randomized trial develops arithmetic theory of critical p-adic L-functions, indicating new insights in number theory.

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Benois et al. (2026) studied this question.

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