On the Reduction of Hyperelliptic Integrals (P=3) To Elliptic Integrals by Transformation of the Second and Third Degrees: A Dissertation (Classic Reprint) - Softcover
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.
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1816-1868
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On the Reduction of Hyperelliptic Integrals (P=3) To Elliptic Integrals by
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Paperback. Condition: New. Print on Demand. This book investigates hyperelliptic integrals of genus 3 using rational transformations. It explores the history of the subject and introduces a method leveraging cubic involutions to solve the problem of their reduction to elliptic integrals. The cubic involution approach allows for a complete study of simultaneous reductions by transformations of the second and third degrees. The author establishes a relationship between the octavic and the branch form, which yields an algebraic condition for the existence of a reducible integral. Notably, the book determines all hyperelliptic integrals reducible to elliptic integrals by transformations of any degree, for a specific curve. Its insights shed light on the problem of reduction, offering an alternative perspective on a classic mathematical problem. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781333272562_0
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On the Reduction of Hyperelliptic Integrals P3 To Elliptic Integrals by Transformation of the Second and Third Degrees A Dissertation Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333272562
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On the Reduction of Hyperelliptic Integrals P3 To Elliptic Integrals by Transformation of the Second and Third Degrees A Dissertation Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333272562
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