Gross–Zagier formula

Target entity: Gross–Zagier formula
Context triple: [Benedict Gross, notableWork, Gross–Zagier formula]

• A. Bloch–Kato conjecture
  The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
• B. Siegel’s theorem on zeros of L-functions
  Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
• C. Birch and Swinnerton-Dyer Conjecture
  The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
• D. Ribet's theorem
  Ribet's theorem is a result in number theory that linked certain modular forms to Galois representations and played a crucial role in the proof of Fermat's Last Theorem.
• E. Fontaine–Mazur conjecture
  The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Gross–Zagier formula
Target entity description: The Gross–Zagier formula is a fundamental result in number theory that relates the heights of Heegner points on elliptic curves to the derivatives of associated L-functions, with deep implications for the Birch and Swinnerton-Dyer conjecture.

• A. Bloch–Kato conjecture
  The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
• B. Siegel’s theorem on zeros of L-functions
  Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
• C. Birch and Swinnerton-Dyer Conjecture
  The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
• D. Ribet's theorem
  Ribet's theorem is a result in number theory that linked certain modular forms to Galois representations and played a crucial role in the proof of Fermat's Last Theorem.
• E. Fontaine–Mazur conjecture
  The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
• F. None of above. chosen