Modular Degrees of Elliptic Curves and Some Quotient of L-values

Hiro Aki Narita, Kousuke Sugimoto

研究成果: Article査読

抄録

By the modular degree we mean the degree of a modular parametrization of an elliptic curve, namely the mapping degree of the surjection from a modular curve to an elliptic curve. Its arithmetic significance is discussed by Zagier and Agashe-Ribet-Stein et al. in terms of the congruence of modular forms. Given an elliptic curve Ef attached to a rational newform f , we explicitly relate its modular degree to a quotient of special values of some two L-functions attached to f . We also provide several numerical examples of the formula.

本文言語English
ページ(範囲)279-293
ページ数15
ジャーナルTokyo Journal of Mathematics
43
2
DOI
出版ステータスPublished - 2020 12

ASJC Scopus subject areas

  • 数学 (全般)

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