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July 12, 2026Memoirs of the American Mathematical Society

Arithmetic of Critical š‘-Adic šæ-Functions

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Authors

DBDenis BenoisKBKĆ¢zım BĆ¼yĆ¼kboduk

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Overview

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

Key Points

  • The research aims to develop a complete arithmetic theory of critical p-adic L-functions on the eigencurve.
  • Developed an Ć©tale 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.

Cite This Study

Benois et al. (2026) studied this question.

synapsesocial.com/papers/6a5334194f7abc118adee288https://doi.org/10.1090/memo/1635
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