The Elliptic Modular Functions Associated With the Elliptic Norm Curve E7 (Classic Reprint) - Softcover

Roscoe Woods

Softcover

ISBN 10: 0366718487 ISBN 13: 9780366718481

Publisher: Forgotten Books, 2018

Synopsis

Delve into the world of elliptic modular functions and the geometry of elliptic norm curves.

This book-length study presents how a family of curves, their symmetries, and their modular functions weave together. It uses group theory and geometry to uncover deep structure behind the elliptic norm curve E' and the related Klein’s quartic, offering a comprehensive view of the subject for curious readers.

The text outlines the builders of the theory: the groups of collineations acting on the curves, canonical forms, and the way the family of curves changes with a modular parameter. It explains how modular functions arise from the geometry, and how projections into different spaces reveal the quadrics, polar conics, and the nets that organize the theory. Throughout, the work ties classical results to new observations about the structure and invariants of these curves.

• Track how the 8 cyclic subgroups and their dihedral companions organize symmetries of the elliptic curves.
• See how a Kleinian form remains invariant under isomorphic groups and how this leads to fundamental elliptic modular functions.
• Learn how projections to spaces S2 and S3 generate polar conics, quadrics, and the base curves of quadratic systems.
• Understand the role of Klein’s quartic K as the locus of a zero point and its connection to modular lines and modular functions.

Ideal for readers of advanced mathematics, deepening an appreciation for the connections between algebra, geometry, and number theory within the history of elliptic modular functions.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0366718487
• ISBN 13: 9780366718481
• Binding: Paperback
• Number of pages: 32