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Discover the arithmetic theory of quaternion algebras and orders with this comprehensive open access textbook. Ideal for graduate students and researchers in algebra, geometry, and number theory, “Quaternion Algebras” offers a unified treatment synthesizing results from across the literature. Explore foundational concepts, arithmetic properties, analytic aspects like zeta functions and idelic approaches, and applications in hyperbolic geometry, low-dimensional topology, and arithmetic geometry. This essential reference, part of the Graduate Texts in Mathematics series, provides numerous pathways for exploration and course construction. It connects quaternionic aspects of modular forms, supersingular elliptic curves, and QM abelian surfaces, making it a valuable resource for understanding diverse mathematical fields.
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