A First Course in Modular Forms
Book
Domain Context
Number Theory and Analysis
Citation
Fred Diamond and Jerry Shurman. (2005). A First Course in Modular Forms. 228. Springer.
Why this reference is included
Diamond and Shurman’s A First Course in Modular Forms (2005), published by Springer, sits in the program’s reference corpus as a standing technical source. Cited 2 times in Book II (Categorical Holomorphy), Part 10, Chapter BSD Bridge: Proto-Rationality in Split-Complex Regime, where the program draws on it in the context of “Elliptic curves. An elliptic curve E / is a smooth projective curve of genus 1 defined over with a specified rational point.”
Cited in
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Book II — Categorical Holomorphy Part 10Chapter BSD Bridge: Proto-Rationality in Split-Complex Regime
Elliptic curves. An elliptic curve E / is a smooth projective curve of genus 1 defined over with a specified rational point
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Book II — Categorical Holomorphy Part 10Chapter BSD Bridge: Proto-Rationality in Split-Complex Regime
The known cases (r_an ≤ 1, by Gross–Zagier and Kolyvagin) use deep machinery from algebraic geometry and the theory of modular forms