Modular invariants for genus 3 hyperelliptic curves

DOI10.1007/s40993-018-0146-6zbMath1420.14063arXiv1807.08986OpenAlexW2883372186WikidataQ128642973 ScholiaQ128642973MaRDI QIDQ2316326

Pınar Kılıçer, Maike Massierer, Sorina Ionica, Elisa Lorenzo García, Christelle Vincent, Adelina Mânzăţeanu, Kristin E. Lauter

Publication date: 26 July 2019

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.08986

zbMATH Keywords

hyperelliptic curvesSiegel modular formsinvariants of binary forms

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Period matrices, variation of Hodge structure; degenerations (32G20) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Theta functions and abelian varieties (14K25) Complex multiplication and moduli of abelian varieties (11G15) Theta functions and curves; Schottky problem (14H42)

Related Items (2)

Isogenous hyperelliptic and non-hyperelliptic Jacobians with maximal complex multiplication ⋮ On different expressions for invariants of hyperelliptic curves of genus 3

Uses Software

• genus3
• hcperiods
• WIN4
• curve_reconstruction

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Teichmüller modular forms
• Theta constants and Teichmüller modular forms
• Slope of cusp forms and theta series
• The hyperelliptic locus
• Theta functions on Riemann surfaces
• Jacobians among Abel threefolds: a formula of Klein and a question of Serre
• Class invariants for quartic CM fields
• Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects
• The CM class number one problem for curves of genus 2
• Generalized Tate curve and integral Teichmuller modular forms
• Constructing genus-3 hyperelliptic Jacobians with CM
• COMPUTINGL-FUNCTIONS AND SEMISTABLE REDUCTION OF SUPERELLIPTIC CURVES
• Chabauty–Coleman Experiments for Genus 3 Hyperelliptic Curves
• On Siegel Modular Forms of Degree Three
• Explicit Hyperelliptic Curves With Real Multiplication and Permutation Polynomials
• On the Discriminant of a Hyperelliptic Curve
• Teichmuller Modular Forms of Degree 3
• Plane quartics over $\mathbb {Q}$ with complex multiplication
• A bound on the primes of bad reduction for CM curves of genus 3
• Modular Forms and Projective Invariants
• On the Graded Ring of Invariants of Binary Octavics
• Hyperelliptic modular curves

This page was built for publication: Modular invariants for genus 3 hyperelliptic curves