Advanced Analytic Number Theory: L-functions by Carlos Moreno
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.-
Quantum Field Theory
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The Cremona Group and Its Subgroups
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Fokker-Planck-Kolmogorov Equations
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Grid Homology for Knots and Links
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The Classification of the Finite Simple Groups, Number 6
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The Classification of the Finite Simple Groups, Number 7
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Braid and Knot Theory in Dimension Four
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Residuated Structures in Algebra and Logic
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Attractors for Degenerate Parabolic Type Equations
- Geometric Function Theory in the Unit Ball of $\mathbb{C}^n$
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Cohen-Macaulay Representations
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The Convenient Setting of Global Analysis
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Noncommutative Multivariable Operator Theory
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Singular Time-Homogeneous Ito Equations and PDEs
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Locally Solid Riesz Spaces with Applications to Economics
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Control and Nonlinearity
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Mixed Motives
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Ergodic Theory Via Joinings
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Ricci Solitons in Dimensions $4$ and Higher
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Vertex Algebras and Algebraic Curves
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Surgery on Compact Manifolds
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Univalent Functions in Quantum Probability Theory
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Perfectoid Spaces
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The Ricci Flow: Techniques and Applications
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Parabolic Geometries I
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Trees of Hyperbolic Spaces
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Foundations of Arithmetic Differential Geometry
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Algebraic Geometry for Scientists and Engineers
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Operators, Functions, and Systems
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Mirror Symmetry and Algebraic Geometry
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Geometric Analysis on Symmetric Spaces
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Self-Similar Groups
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Knotted Surfaces and Their Diagrams
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Alice and Bob Meet Banach
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Weak Convergence of Measures
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Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups
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Iwasawa Theory and Its Perspective, Volume 1
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Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators
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The Classification of the Finite Simple Groups, Number 10
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Chaotic Billiards
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Automorphic Forms Beyond $\mathrm {GL}_2$
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Painleve Transcendents
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Applications of Group Theory in Cryptography
| SKU | Unavailable |
| ISBN 13 | 9780821842669 |
| ISBN 10 | 0821842668 |
| Title | Advanced Analytic Number Theory: L-functions |
| Author | Carlos Moreno |
| Series | Mathematical Surveys And Monographs |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | American Mathematical Society |
| Year published | 2005-01-30 |
| Number of pages | 291 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |