A twisted adjoint \(L\)-value of an elliptic modular form
type: Item
instance of: scholarly article
title: A twisted adjoint \(L\)-value of an elliptic modular form
zbMATH Open document ID: 0924.11036
author: Keiji Goto
published in: Journal of Number Theory
publication date: 1999-11-15T00:00:00Z
review text: Let \(f\) be a primitive elliptic cusp form and let \(\chi\) be a quadratic character. Consider the twisted adjoint \(L\)-function \(L(s, \text{Ad}(f)\otimes \chi)\) for \(f\) and \(\chi\). It has been conjectured that the special value of \(L(s, \text{Ad}(f)\otimes \chi)\) at \(s=1\) is closely related to the discriminant of Hecke fields by \textit{K. Doi, H. Hida} and \textit{H. Ishii} [Invent. Math. 134, 547-577 (1998; Zbl 0924.11035 above)]. The author of this paper calculates the numerical examples of the calculations of special values of the twisted adjoint \(L\)-function \(L(s, \text{Ad}(f) \otimes\chi)\) and proves that they support the conjecture.
reviewed by: Masakazu Muro
Mathematics Subject Classification ID: 11F67
zbMATH DE Number: 1268043
zbMATH Keywords: elliptic cusp form
zbMATH Keywords: twisted adjoint \(L\)-function
zbMATH Keywords: special value
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: jnth.1998.2270
OpenAlex ID: W1976420216
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DOI: 10.1006/JNTH.1998.2270
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description: scientific article; zbMATH DE number 1268043