Atjaunināt sīkdatņu piekrišanu

Automorphic Forms and L-Functions for the Group GL(n,R) [Mīkstie vāki]

5.00/5 (3 ratings by Goodreads)
(Columbia University, New York)
  • Formāts: Paperback / softback, 516 pages, height x width x depth: 227x151x29 mm, weight: 740 g, Worked examples or Exercises; 1 Line drawings, black and white
  • Sērija : Cambridge Studies in Advanced Mathematics
  • Izdošanas datums: 26-Nov-2015
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1107565022
  • ISBN-13: 9781107565029
Citas grāmatas par šo tēmu:
  • Mīkstie vāki
  • Cena: 76,82 €
  • Grāmatu piegādes laiks ir 3-4 nedēļas, ja grāmata ir uz vietas izdevniecības noliktavā. Ja izdevējam nepieciešams publicēt jaunu tirāžu, grāmatas piegāde var aizkavēties.
  • Daudzums:
  • Ielikt grozā
  • Piegādes laiks - 4-6 nedēļas
  • Pievienot vēlmju sarakstam
Automorphic Forms and L-Functions for the Group GL(n,R)Palielināt
  • Formāts: Paperback / softback, 516 pages, height x width x depth: 227x151x29 mm, weight: 740 g, Worked examples or Exercises; 1 Line drawings, black and white
  • Sērija : Cambridge Studies in Advanced Mathematics
  • Izdošanas datums: 26-Nov-2015
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1107565022
  • ISBN-13: 9781107565029
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781107565029.html
Keywords:
L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with basic knowledge of classical analysis, complex variable theory, and algebra.

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.

Recenzijas

' a gentle introduction to this fascinating new subject. The presentation is very explicit and many examples are worked out with great detail This book should be of great interest to students beginning with the theory of modular forms or for more advanced readers wanting to know about general L-functions.' Emmanuel P. Royer, Mathematical Reviews 'This book, whose clear and sometimes simplified proofs make the basic theory of automorphic forms on GL(n) accessible to a wide audience, will be valuable for students. It nicely complements D. Bump's book (Automorphic Forms and Representations, Cambridge, 1997), which offers a greater emphasis on representation theory and a different selection of topics.' Zentralblatt MATH 'Unfortunately, when n > 2 the GL(n) theory is not very accessible to the student of analytic number theory, yet it is increasing in importance. [ This book] addresses this problem by developing a large part of the theory in a way that is carefully designed to make the field accessible much of the literature is written in the adele language, and seeing how it translates into classical terms is both useful and enlightening This is a unique and very welcome book, one that the student of automorphic forms will want to study, and also useful to experts.' Daniel Bump, SIAM Review

Papildus informācija

This book presents a self-contained graduate-level introduction to the topic of L-functions.
Introduction xi
1 Discrete group actions
1(37)
1.1 Action of a group on a topological space
3(5)
1.2 Iwasawa decomposition
8(7)
1.3 Siegel sets
15(4)
1.4 Haar measure
19(4)
1.5 Invariant measure on coset spaces
23(4)
1.6 Volume of SL(n, Z)\SL(n, R)/SO(n, R)
27(11)
2 Invariant differential operators
38(16)
2.1 Lie algebras
39(3)
2.2 Universal enveloping algebra of gl(n, R)
42(4)
2.3 The center of the universal enveloping algebra of gl(n, R)
46(4)
2.4 Eigenfunctions of invariant differential operators
50(4)
3 Automorphic forms and L--functions for SL(2, Z)
54(45)
3.1 Eisenstein series
55(4)
3.2 Hyperbolic Fourier expansion of Eisenstein series
59(3)
3.3 Maass forms
62(1)
3.4 Whittaker expansions and multiplicity one for GL(2, M)
63(4)
3.5 Fourier--Whittaker expansions on GL(2, R)
67(1)
3.6 Ramanujan--Petersson conjecture
68(2)
3.7 Selberg eigenvalue conjecture
70(1)
3.8 Finite dimensionality of the eigenspaces
71(2)
3.9 Even and odd Maass forms
73(1)
3.10 Hecke operators
74(3)
3.11 Hermite and Smith normal forms
77(3)
3.12 Hecke operators for 2(SL(2, Z))\h2
80(4)
3.13 L--functions associated to Maass forms
84(5)
3.14 L-functions associated to Eisenstein series
89(2)
3.15 Converse theorems for SL(2, Z)
91(3)
3.16 The Selberg spectral decomposition
94(5)
4 Existence of Maass forms
99(15)
4.1 The infinitude of odd Maass forms for SL(2, Z)
100(1)
4.2 Integral operators
101(4)
4.3 The endomorphism ♥
105(1)
4.4 How to interpret ♥: an explicit operator with purely cuspidal image
106(2)
4.5 There exist infinitely many even cusp forms for SL(2, Z)
108(2)
4.6 A weak Weyl law
110(1)
4.7 Interpretation via wave equation and the role of finite propagation speed
111(1)
4.8 Interpretation via wave equation: higher rank case
111(3)
5 Maass forms and Whittaker functions for SL(n, Z)
114(39)
5.1 Maass forms
114(2)
5.2 Whittaker functions associated to Maass forms
116(2)
5.3 Fourier expansions on SL(n, Z)\hn
118(10)
5.4 Whittaker functions for SL(n, R)
128(1)
5.5 Jacquet's Whittaker function
129(5)
5.6 The exterior power of a vector space
134(4)
5.7 Construction of the IV Function using wedge products
138(3)
5.8 Convergence of Jacquet's Whittaker function
141(3)
5.9 Functional equations of Jacquet's Whittaker function
144(6)
5.10 Degenerate Whittaker functions
150(3)
6 Automorphic forms and L-functions for SL (3, Z)
153(41)
6.1 Whittaker functions and multiplicity one for SL(3, Z)
153(6)
6.2 Maass forms for SL(3, Z)
159(2)
6.3 The dual and symmetric Maass forms
161(2)
6.4 Hecke operators for SL(3, Z)
163(9)
6.5 The Godement--Jacquet L-function
172(14)
6.6 Bump's double Dirichlet series
186(8)
7 The Gelbart--Jacquet lift
194(41)
7.1 Converse theorem for SL (3, Z)
194(16)
7.2 Rankin--Selberg convolution for GL(2)
210(3)
7.3 Statement and proof of the Gelbart--Jacquet lift
213(10)
7.4 Rankin--Selberg convolution for GL(3)
223(12)
8 Bounds for L-functions and Siegel zeros
235(24)
8.1 The Selberg class
235(3)
8.2 Convexity bounds for the Selberg class
238(3)
8.3 Approximate functional equations
241(4)
8.4 Siegel zeros in the Selberg class
245(4)
8.5 Siegel's theorem
249(2)
8.6 The Siegel zero lemma
251(1)
8.7 Non-existence of Siegel zeros for Gelbart--Jacquet lifts
252(4)
8.8 Non-existence of Siegel zeros on GL(n)
256(3)
9 The Godement--Jacquet L-function
259(26)
9.1 Maass forms for SL(n, Z)
259(2)
9.2 The dual and symmetric Maass forms
261(5)
9.3 Hecke operators for SL(n, Z)
266(11)
9.4 The Godement--Jacquet L-function
277(8)
10 Langlands Eisenstein series
285(52)
10.1 Parabolic subgroups
286(2)
10.2 Langlands decomposition of parabolic subgroups
288(4)
10.3 Bruhat decomposition
292(3)
10.4 Minimal, maximal, and general parabolic Eisenstein series
295(6)
10.5 Eisenstein series twisted by Maass forms
301(2)
10.6 Fourier expansion of minimal parabolic Eisenstein series
303(4)
10.7 Meromorphic continuation and functional equation of maximal parabolic Eisenstein series
307(3)
10.8 The L-function associated to a minimal parabolic Eisenstein series
310(5)
10.9 Fourier coefficients of Eisenstein series twisted by Maass forms
315(4)
10.10 The constant term
319(2)
10.11 The constant term of SL(3, Z) Eisenstein series twisted by SL(2, Z)-Maass forms
321(1)
10.12 An application of the theory of Eisenstein series to the non-vanishing of L-functions on the line (s) = 1
322(2)
10.13 Langlands spectral decomposition for SL(3, Z)\h3
324(13)
11 Poincare series and Kloosterman sums
337(28)
11.1 Poincare series for SL(n, Z)
337(2)
11.2 Kloosterman sums
339(4)
11.3 Plucker coordinates and the evaluation of Kloosterman sums
343(7)
11.4 Properties of Kloosterman sums
350(2)
11.5 Fourier expansion of Poincare series
352(2)
11.6 Kuznetsov's trace formula for SL(n, Z)
354(11)
12 Rankin--Selberg convolutions
365(30)
12.1 The GL(n) × GL(n) convolution
366(6)
12.2 The GL(n) × GL(n + 1) convolution
372(4)
12.3 The GL(n) × GL(n') convolution with n < n'
376(5)
12.4 Generalized Ramanujan conjecture
381(3)
12.5 The Luo--Rudnick--Sarnak bound for the generalized Ramanujan conjecture
384(9)
12.6 Strong multiplicity one theorem
393(2)
13 Langlands conjectures
395(12)
13.1 Artin L-functions
397(5)
13.2 Langlands functoriality
402(5)
List of symbols
407(2)
Appendix The GL(n)pack Manual Kevin A. Broughan
409(64)
A.1 Introduction
409(4)
A.2 Functions for GL(n)pack
413(3)
A.3 Function descriptions and examples
416(57)
References 473(12)
Index 485(10)
Errata 495