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Elementary Theory of L-functions and Eisenstein Series / Haruzo Hida.

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An elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise.

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Bibliographic Details
Online Access: Full Text (via Cambridge)
Main Author: Hida, Haruzo
Format: Electronic eBook
Language:English
Published: Cambridge : Cambridge University Press, 1993.
Series:London Mathematical Society student texts ; no. 26.
Subjects:
L-functions.
Eisenstein series.

MARC

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245 1 0 |a Elementary Theory of L-functions and Eisenstein Series /  |c Haruzo Hida. 
260 |a Cambridge :  |b Cambridge University Press,  |c 1993. 
300 |a 1 online resource (400 pages) 
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337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a London Mathematical Society Student Texts ;  |v no. 26 
500 |a Title from publishers bibliographic system (viewed 22 Dec 2011). 
520 |a An elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise. 
504 |a Includes bibliographical references (pages 365-370) and index. 
505 0 |a Cover -- Title -- Copyright -- Contents -- Preface -- Suggestions to the reader -- Chapter 1. Algebraic Number Theory -- 1.1. Linear algebra over rings -- 1.2. Algebraic number fields -- 1.3. p-adic numbers -- Chapter 2. Classical L-functions and Eisenstein series -- 2.1. Euler's method -- 2.2. Analytic continuation and the functional equation -- 2.3. Hurwitz and Dirichlet L-functions -- 2.4. Shintani L-functions -- 2.5. L-functions of real quadratic field -- 2.6. L-functions of imaginary quadratic fields -- 2.7. Hecke L-functions of number fields. 
505 8 |a Chapter 3. p-adic Hecke L-functions -- 3.1. Interpolation series -- 3.2. Interpolation series in p-adic fields -- 3.3. p-adic measures on Zp -- 3.4. The p-adic measure of the Riemann zeta function -- 3.5. p-adic Dirichlet L-functions -- 3.6. Group schemes and formal group schemes -- 3.7. Toroidal formal groups and p-adic measures -- 3.8. p-adic Shintani L-functions of totally real fields -- 3.9. p-adic Hecke L-functions of totally real fields -- Chapter 4. Homological Interpretation -- 4.1. Cohomology groups on Gm(C) -- 4.2. Cohomological interpretation of Dirichlet L-values. 
505 8 |a 4.3. p-adic measures and locally constant functions -- 4.4. Another construction of p-adic Dirichlet L-functions -- Chapter 5. Elliptic modular forms and their L-functions -- 5.1. Classical Eisenstein series of GL(2)/Q -- 5.2. Rationality of modular forms -- 5.3. Hecke operators -- 5.4. The Petersson inner product and the Rankin product -- 5.5. Standard L-functions of holomorphic modular forms -- Chapter 6. Modular forms and cohomology groups -- 6.1. Cohomology of modular groups -- 6.2. Eichler-Shimura isomorphisms -- 6.3. Hecke operators on cohomology groups. 
505 8 |a 6.4. Algebraicity theorem for standard L-functions of GL(2) -- 6.5. Mazur's p-adic Mellin transforms -- Chapter 7. Ordinary A-adic forms, two variable p-adic Rankin products and Galois representations -- 7.1. p-Adic families of Eisenstein series -- 7.2. The projection to the ordinary part -- 7.3. Ordinary A-adic forms -- 7.4. Two variable p-adic Rankin product -- 7.5. Ordinary Galois representations into GL2(ZP[[X]]) -- 7.6. Examples of A-adic forms -- Chapter 8. Functional equations of Hecke L-functions -- 8.1. Adelic interpretation of algebraic number theory. 
505 8 |a 8.2. Hecke characters as continuous idele characters -- 8.3. Self-duality of local fields -- 8.4. Haar measures and the Poisson summation formula -- 8.5. Adelic Haar measures -- 8.6. Functional equations of Hecke L-functions -- Chapter 9. Adelic Eisenstein series and Rankin products -- 9.1. Modular forms on GL2(FA) -- 9.2. Fourier expansion of Eisenstein series -- 9.3. Functional equation for Eisenstein series -- 9.4. Analytic continuation of Rankin products -- 9.5. Functional equations for Rankin products -- Chapter 10. Three variable p-adic Rankin products. 
650 0 |a L-functions. 
650 0 |a Eisenstein series. 
650 7 |a Eisenstein series.  |2 fast  |0 (OCoLC)fst00904095 
650 7 |a L-functions.  |2 fast  |0 (OCoLC)fst00989693 
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830 0 |a London Mathematical Society student texts ;  |v no. 26. 
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