Quaternion Algebras by John Voight
Quaternion Algebras - Table of Contents
PART I: ALGEBRA
- 2. Beginnings
- 3. Involutions
- 4. Quadratic Forms
- 5. Ternary Quadratic Forms & Quaternion Algebras
- 6. Characteristic
- 7. Simple Algebras
- 8. Simple Algebras and Involutions
PART II: ARITHMETIC
- 9. Lattices and Integral Quadratic Forms
- 10. Quaternion Orders
- 11. The Hurwitz Order
- 12. Ternary Quadratic Forms Over Local Fields
- 13. Quaternion Algebras Over Local Fields
- 14. Quaternion Algebras Over Global Fields
- 15. Discriminants
- 16. Quaternion Ideals and Invertibility
- 17. Classes of Quaternion Ideals
- 18. Two-Sided Ideals and the Picard Group
- 19. Brandt Groupoids
- 20. Integral Representation Theory
- 21. Hereditary and Extremal Orders
- 22. Quaternion Orders & Ternary Quadratic Forms
- 23. Quaternion Orders
- 24. Quaternion Orders: Second Meeting
PART III: ANALYSIS
- 25. The Eichler Mass Formula
- 26. Classical Zeta Functions
- 27. Adelic Framework
- 28. Strong Approximation
- 29. Idelic Zeta Functions
- 30. Optimal Embeddings
- 31. Selectivity
PART IV: GEOMETRY AND TOPOLOGY
- 32. Unit Groups
- 33. Hyperbolic Plane
- 34. Discrete Group Actions
- 35. Classical Modular Group
- 36. Hyperbolic Space
- 37. Fundamental Domains
- 38. Arithmetic Groups
- 39. Volume Formula
PART V: ARITHMETIC GEOMETRY
- 40. Classical Modular Forms
- 41. Brandt Matrices
- 42. Supersingular Elliptic Curves
- 43. QM Abelian Surfaces
What You Will Learn in Quaternion Algebras
Quaternion Algebras by John Voight is an authoritative, modern open-access textbook published in the prestigious Graduate Texts in Mathematics series. Designed for advanced graduate students and researchers in number theory and arithmetic geometry, this volume provides a unifying framework for quaternion algebras and non-commutative arithmetic problem solving practice.
The textbook systematically covers central simple algebras, Hamilton's quaternions, Hilbert symbols, maximal orders, class numbers, Brandt matrices, arithmetic Fuchsian groups, Shimura curves, and modular forms. By connecting non-commutative algebra with Riemannian geometry and automorphic forms, Voight enables readers to execute complex arithmetic structure computations and quaternion lattice proofs with precision.
Treasured globally by number theorists and algebraists for its exceptional structural clarity and rich historical context, this modern monograph serves as an outstanding self-study guide. Voight’s comprehensive exposition equips learners with vital mathematical tools required for mastering modern arithmetic quaternion principles.
Book Details & Specifications
Title:
Quaternion Algebras by John Voight
Publisher:
Springer
Year:
2022
Pages:
908
Type:
PDF
Language:
English
ISBN-10 #:
3030574679
ISBN-13 #:
978-3030574673
License:
CC BY-NC 4.0
Amazon:
Amazon
About the Author: John Voight
The author John Voight
is a Professor of Mathematics at Dartmouth College, internationally recognized for his research in computational number theory, arithmetic geometry, and explicit methods for automorphic forms and quaternion algebras.
His academic works stand as authoritative quaternion algebras, arithmetic geometry, and computational number theory study guides.
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