Here is the statement as I understand it to be, framed as a bijection of sets. My chief reference is the wonderful book Elliptic Curves, Modular Forms and their L-Functions by Álvaro Lozano-Robledo ...

Image Credit: The header image has been taken from Quanta Magazine (New Proof Distinguishes Mysterious and Powerful 'Modular Forms') At the end of February this year (2024), I finished (re-)learning ...

この命題は、「数学の異なる領域に存在する対称性の統一」という本質を持つ。より具体的には、数論的対象（楕円曲線やアーベル多様体）に潜む対称性（ガロワ群の表現）と、解析的対象（保型形式）に潜む対称性（保型表現）が、実は同じものであると ...

The modularity theorem implies that for every elliptic curve \(E /\mathbb{Q}\) there exist rational maps from the modular curve \(X_0(N)\) to \(E\), where \(N\) is ...

This is an elliptic curve over ℚ. By the Modularity Theorem — the theorem Wiles proved to establish Fermat's Last Theorem — TH (a,d) corresponds to a Hecke eigenform on the modular surface M = SL (2,ℤ ...

Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there ...

1 Department of Chemistry and Nanoscience, GLA University, Mathura, India. 2 Agriculture and Ecology Research Unit, Indian Statistical Institute, Kolkata, India. British mathematician Andrew Wiles ...

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