On the Reduction of Hyperelliptic Integrals (P=3) To Elliptic Integrals by Transformation of the Second and Third Degrees: A Dissertation (Classic Reprint) - Hardcover

William Gillespie

Hardcover

ISBN 10: 0484628976 ISBN 13: 9780484628976

Publisher: Forgotten Books, 2018

Synopsis

A rigorous study showing how certain hyperelliptic integrals can be transformed into elliptic ones by rational changes of degree three and two.

The work delves into the structure of reducible integrals, explores cubic involutions, and develops normal forms. It also applies the Weierstrass–Picard period approach to specific curves, revealing how transformations of various degrees interact with the integral’s geometry.

• How a hyperelliptic integral of genus three can be reduced to elliptic form via a third‑degree transformation.
• The role of cubic involutions, branch points, and pairing of double points in reducibility.
• A normal form for reducible integrals and the conditions that guarantee a reduction.
• Use of period theory to analyze reductions and the explicit expression of transformed integrals.

Ideal for readers of advanced mathematics who want a detailed, method‑driven treatment of reduction techniques and period theory in hyperelliptic contexts.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0484628976
• ISBN 13: 9780484628976
• Binding: Hardcover
• Number of pages: 49