@article{1431086,
      author = {Voight, John,},
      url = {http://library.usi.edu/record/1431086},
      title = {Quaternion algebras /},
      abstract = {This open access textbook presents a comprehensive  treatment of the arithmetic theory of quaternion algebras  and orders, a subject with applications in diverse areas of  mathematics. Written to be accessible and approachable to  the graduate student reader, this text collects and  synthesizes results from across the literature. Numerous  pathways offer explorations in many different directions,  while the unified treatment makes this book an essential  reference for students and researchers alike. Divided into  five parts, the book begins with a basic introduction to  the noncommutative algebra underlying the theory of  quaternion algebras over fields, including the relationship  to quadratic forms. An in-depth exploration of the  arithmetic of quaternion algebras and orders follows. The  third part considers analytic aspects, starting with zeta  functions and then passing to an idelic approach, offering  a pathway from local to global that includes strong  approximation. Applications of unit groups of quaternion  orders to hyperbolic geometry and low-dimensional topology  follow, relating geometric and topological properties to  arithmetic invariants. Arithmetic geometry completes the  volume, including quaternionic aspects of modular forms,  supersingular elliptic curves, and the moduli of QM abelian  surfaces.},
      doi = {https://doi.org/10.1007/978-3-030-56694-4},
      recid = {1431086},
      pages = {1 online resource},
}