The standard L-function attached to a vector valued modular form

2024/11/03 by Oliver Stein, Stein, Oliver
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2411.01620

openalex publication_date 2024/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define two L-functions associated to a common vector valued eigenform f transforming with the ``finite'' Weil representation. The first one can be seen as a standard zeta function defined by the eigenvalues of f. The second one can be interpreted as standard L-function defined as an Euler product where each p-factor is a rational function in terms of two unramified characters of the p-adic field \Q_p. We show that both L-functions are related and prove further that they both can be continued meromorphically to the whole complex s-plane.

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