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math.NT2026
Local statistics and average rank of genus hyperelliptic curves with a Weierstrass point
Keunyoung Jeong, Junyeong Park
In this paper, we determine the probability that a genus hyperelliptic curve with a Weierstrass point over a number field has good reduction at a given prime of residue charact…
math.NT2026
Arithmetic BF theory and the Cassels-Tate pairing
Jeehoon Park, Junyeong Park
We give a systematic treatment of the arithmetic BF theory, introduced by Carlson and Kim. We observe that the Cassels-Tate pairing can be naturally interpreted as an arithmetic BF…
math.NT2026
Goldfeld conjecture for non-hyperelliptic direction
Keunyoung Jeong, Junyeong Park
Since the curve has a large automorphism group, there exist twist families arising from non-hyperelliptic directions. In this paper, we give an explicit upper bound o…