{"product_id":"advanced-analytic-number-theory-l-functions","title":"Advanced Analytic Number Theory: L-functions","description":"Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations.The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":57186359509336,"sku":"9780821842669","price":122.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9780821842669_a7373941-9c2d-42e1-b228-35779f5c9d0d.jpg?v=1780110945","url":"https:\/\/agendabookshop.com\/products\/advanced-analytic-number-theory-l-functions","provider":"Agenda Bookshop","version":"1.0","type":"link"}