Description
Explore the intricate world of number theory with 'Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula.' This essential volume, published by Princeton University Press, delves deep into Robert Langlands’ groundbreaking functoriality principle. With an ISBN of 9780691085180 and a publication year of 1989, this trade paperback is a must-have for both researchers and enthusiasts in the field of automorphic forms and arithmetic subgroups.
The book systematically unravels the relationships between automorphic forms on various arithmetic subgroups of reductive groups. Specifically, it examines the base change problem for GL(n), offering readers a comprehensive understanding of how these forms relate across cyclic extensions of number fields. The authors leverage powerful results from the last two decades of research, effectively communicating complex ideas in a manner accessible to knowledgeable readers eager to expand their understanding of advanced number theory. Although it does not serve as a beginner's guide, it provides thorough references that enhance both learning and research in the theory of automorphic forms.
This BRAND NEW book is a valuable addition to your academic library, perfect for graduate students and mathematical researchers alike. Note: Shipping for this item is free. Please allow up to 6 weeks for delivery. Once your order is placed, it cannot be cancelled.
Note: Shipping for this item is free. Please allow up to 6 weeks for delivery. Once your order is placed, it cannot be cancelled.
Condition: BRAND NEW
ISBN: 9780691085180
Format: Trade paperback (US)
Year: 1989
Publisher: Princeton University Press
Description:
A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.
The book systematically unravels the relationships between automorphic forms on various arithmetic subgroups of reductive groups. Specifically, it examines the base change problem for GL(n), offering readers a comprehensive understanding of how these forms relate across cyclic extensions of number fields. The authors leverage powerful results from the last two decades of research, effectively communicating complex ideas in a manner accessible to knowledgeable readers eager to expand their understanding of advanced number theory. Although it does not serve as a beginner's guide, it provides thorough references that enhance both learning and research in the theory of automorphic forms.
This BRAND NEW book is a valuable addition to your academic library, perfect for graduate students and mathematical researchers alike. Note: Shipping for this item is free. Please allow up to 6 weeks for delivery. Once your order is placed, it cannot be cancelled.
Note: Shipping for this item is free. Please allow up to 6 weeks for delivery. Once your order is placed, it cannot be cancelled.
Condition: BRAND NEW
ISBN: 9780691085180
Format: Trade paperback (US)
Year: 1989
Publisher: Princeton University Press
Description:
A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.