Automorphic Forms and Representations

This book serves as a comprehensive introduction to automorphic forms and representations, bridging foundational concepts with advanced research topics.

The theory of automorphic forms stands as a pivotal element in modern number theory and plays a crucial role in the proof of Fermat's Last Theorem. Automorphic Forms and Representations introduces this complex subject in a manner that is approachable for graduate students who are new to the field, while also delving into cutting-edge research topics. The book strikes a balance between being an advanced textbook and a focused monograph, making it suitable for a wide range of readers.

In Automorphic Forms and Representations, readers will explore both classical and representation-theoretic perspectives of automorphic forms. The author emphasizes complete proofs that highlight the unique principles underlying fundamental constructions. The text is rich with foundational material covering the representation theory of GL(1) and GL(2) over local fields, as well as the intricate theory of automorphic representations, L-functions, and advanced topics like the Langlands conjectures and the Rankin–Selberg method.

This comprehensive guide is designed for both researchers and students, providing insights into a notoriously challenging subject. By examining automorphic forms from various complementary viewpoints, Automorphic Forms and Representations equips readers with a robust understanding, guiding them from foundational concepts to the latest developments in the field. It's an essential resource for anyone looking to deepen their knowledge in number theory and related areas.