Automorphic Forms and Even Unimodular Lattices 9783319958903

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Название: Automorphic Forms and Even Unimodular Lattices
ISBN: 9783319958903
Издательство: Springer
Классификация:

Математика

Дискретная математика

Алгебра

Теория чисел

Топология

Информационные технологии: общие вопросы

ISBN-10: 3319958909
Обложка/Формат: Hardcover
Страницы: 417
Вес: 0.95 кг.
Дата издания: 15.03.2019
Серия: Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics
Язык: English
Издание: 1st ed. 2018
Иллюстрации: 1 illustrations, color; 23 illustrations, black and white; xxi, 423 p. 24 illus., 1 illus. in color.
Размер: 165 x 242 x 32
Читательская аудитория: General (us: trade)
Подзаголовок: Kneser neighbors of niemeier lattices
Ссылка на Издательство: Link
Рейтинг:
Поставляется из: Германии
Описание: This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur.Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations.This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
Дополнительное описание: Preface.-1 Introduction.- 2 Bilinear and Quadratic Algebra.- 3 Kneser Neighbors.- 4 Automorphic Forms and Hecke Operators.- 5 Theta Series and Even Unimodular Lattices.- 6 Langlands Parametrization.- 7 A Few Cases of the Arthur–Langlands Conjecture.- 8 Ar

Automorphic Forms and Even Unimodular Lattices,