Galois action on special theta values

2014/09/25 by Paloma Bengoechea, Bengoechea, Paloma · 1 citation
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1409.7214

13 pages, To appear in Journal de Theorie des Nombres de Bordeaux

arxiv created 2014/09/25 · openalex publication_date 2014/09/25 · arxiv updated 2014/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using Shimura's reciprocity law, we calculate the Galois action on the special values of theta functions associated to primitive Dirichlet characters of odd conductor, normalised by the Dedekind eta function, at the point i. As a consequence, we prove some experimental results of Cohen and Zagier and we deduce a partial result on the non-vanishing of these special theta values with prime conductor.

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• Central L values of congruent number elliptic curves

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• Theta operators on Siegel modular forms and Galois representations
• Non vanishing of theta functions and sets of small multiplicative energy
• Theta Functions and Reciprocity Laws
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• On the values of some singular currents on Shimura varieties of orthogonal type