Theta series and number fields: theorems and experiments

DOI10.1007/s11139-021-00394-yzbMath1476.11075arXiv1910.00202OpenAlexW3134089058MaRDI QIDQ2052849

Guillermo Mantilla-Soler, Adrian Barquero-Sanchez, Nathan C. Ryan

Publication date: 29 November 2021

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.00202

zbMATH Keywords

theta seriesquartic fields

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Theta series; Weil representation; theta correspondences (11F27) Quadratic forms over global rings and fields (11E12) Cubic and quartic extensions (11R16)

Uses Software

• SageMath
• LMFDB
• GitHub

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integral trace forms associated to cubic extensions
• Ternary positive definite quadratic forms are determined by their theta series
• Higher composition laws. III: The parametrization of quartic rings
• Algebraic number fields with the discriminant equal to that of a quadratic number field
• A proof of a conjecture on trace-zero forms and shapes of number fields
• The density of discriminants of quartic rings and fields
• On modular forms of half integral weight
• A space of weight one modular forms attached to totally real cubic number fields
• Elliptic Modular Forms and Their Applications
• Levels of positive definite ternary quadratic forms
• A Database for Field Extensions of the Rationals
• Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves
• Reflection Principles and Bounds for Class Group Torsion

This page was built for publication: Theta series and number fields: theorems and experiments