Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Authors: Kiming, I., Rustom, N.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209515
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4 / I. Kiming, N. Rustom // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 28 назв. — англ.

We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function, whereas the characteristic 0 eigenform is attached to an elliptic curve defined over Q. We produce the lift by showin...