Deligne's conjecture on the critical values of Hecke L-functions

2024/06/10 by Han-Ung Kufner, Kufner, Han-Ung · 2 citations
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2406.06148

openalex publication_date 2024/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a proof of Deligne's conjecture on the critical values of L-functions for arbitrary algebraic Hecke characters. This extends a result of Blasius, which only works in the case of CM fields. The key new insight is that the Eisenstein-Kronecker classes of Kings-Sprang, which allow for a cohomological interpretation of the value L(χ,0) for Hecke characters χ of arbitrary totally imaginary fields, can be regarded as de Rham classes of Blasius' reflex motive.

Cited by

• On Deligne's conjecture for Hecke characters
• Period relations for Rankin-Selberg convolutions for GL(n)\timesGL(n)

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