Chapter
§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
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
§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
§5.4. 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
§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
§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
§10.1. Differential operators of Maass and Shimura
§10.2. The algebraicity theorem for Rankin products
§10.3. Two variable A-adic Eisenstein series
§10.4. Three variable p-adic Rankin products
§10.5. Relation to two variable p-adic Rankin products
§10.6. Concluding remarks
Appendix: Summary of homology and cohomology theory
Answers to selected exercises
Elementary Theory of L-functions and Eisenstein Series
( London Mathematical Society Student Texts )
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