On the Jacobian of a family of hyperelliptic curves

MaRDI QIDQ2683729

Donggeon Yhee, Keunyoung Jeong, Junyeong Park

Publication date: 14 February 2023

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.03156

zbMATH Keywords

hyperelliptic curveJacobian\(L\)-functionalgebraic rankparity conjectureanalytic rank

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Theta series; Weil representation; theta correspondences (11F27) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

Uses Software

• SageMath

Cites Work

• Computing a Selmer group of a Jacobian using functions on the curve
• On the arithmetic of the curves \(y^2=x^l+A\). II
• Characterization of the torsion of the Jacobians of two families of hyperelliptic curves
• Theta liftings and Hecke L-functions.
• On the number of rational squares at fixed distance from a fifth power
• On the L -functions of the curves y ² = x ^ℓ + A
• On the arithmetic of the curves o y2 = xℓ + A and their Jacobians
• Nonvanishing of central Hecke L-values and rank of certain elliptic curves
• Eigenfunctions of the Weil representation of unitary groups of one variable
• ON THE L-FUNCTION OF THE CURVES $\lowercase{y}^2 = \lowercase{x}^5 + A$
• On the arithmetic of abelian varieties

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