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## Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier

*Laura Capuano, Peter Jossen, Christina Karolus, and Francesco Veneziano*

### in Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691193779
- eISBN:
- 9780691197548
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691193779.003.0003
- Subject:
- Mathematics, Geometry / Topology

This chapter details Umberto Zannier's minicourse on hyperelliptic continued fractions and generalized Jacobians. It begins by presenting the Pell equation, which was studied by Indian, and later by ... More

## Algebraic Thought in Medieval India

*Victor J. Katz and Karen Hunger Parshall*

### in Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691149059
- eISBN:
- 9781400850525
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149059.003.0006
- Subject:
- Mathematics, History of Mathematics

This chapter explores medieval Indian algebraic thought in the works of Āryabhạta, author of the astronomical treatise Āryabhạtīya (ca. 500 CE), and Brahmagupta, who wrote the ... More

## Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

*Gisbert Wüstholz and Clemens Fuchs (eds)*

- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691193779
- eISBN:
- 9780691197548
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691193779.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the ... More

## Introduction

*Gisbert Wüstholz and Clemens Fuchs (eds)*

### in Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691193779
- eISBN:
- 9780691197548
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691193779.003.0001
- Subject:
- Mathematics, Geometry / Topology

This introductory chapter provides an overview of the three topics discussed in this book: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings heights and ... More

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