1. The Sato-Tate conjecture and Nagao's conjecture
- Author
-
Seoyoung Kim
- Subjects
Algebra and Number Theory ,Mathematics - Number Theory ,Mathematics::Number Theory ,FOS: Mathematics ,Primary 14D10, Secondary 11G35, 11G40, 14G25, 14J27 ,Number Theory (math.NT) - Abstract
Nagao's conjecture relates the rank of an elliptic surface to a limit formula arising from a weighted average of fibral Frobenius traces, and it is further generalized for smooth irreducible projective surfaces by M. Hindry and A. Pacheco. We show that the Sato-Tate conjecture based on the random matrix model implies Nagao's conjecture for certain twist families of elliptic curves and hyperelliptic curves.
- Published
- 2023
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