Heat Eisenstein series on SL[subscript n](C).

Intro -- Contents -- Acknowledgements -- Introduction -- Notation and Terminology -- Chapter 1. Estimates on SL[sub(n)] Parabolics -- 1. The hermitian norm on SL[sub(n)] and Siegel sets -- 2. Volume and lattice point estimates -- 3. Estimates of A-projections -- 4. Standard reduced parabolics -- 5. Characters on parabolics -- 6. Estimates of Ap-projections -- 7. Parabolic integral formulas -- Chapter 2. Eisenstein Series -- 1. The character Eisenstein series -- 2. Twists of character Eisenstein series -- 3. Two-character Eisenstein series -- 4. The Gauss space -- 5. The parabolic Eisenstein integration formula -- Chapter 3. Adjointness and Inversion Relations -- 1. Adjointness formulas and F-cuspidality -- 2. Adjointness and initial conditions formulas -- 3. P-cuspidality and heat Eisenstein series -- 4. The family of anticuspidal operators J[sub(P,Γ,e,t)] -- Chapter 4. Applications of the Heat Equation -- 1. Parabolics and the (a, n)-characters -- 2. Direct image of Casimir on parabolics -- 3. The differential equation for E[sub(P,Γ,K)] and E[sup(#)][sub(P,K)] -- 4. Convolution of Tr[sub(Γ)](K[sub(X)]) and the Eisenstein series -- 5. The P-anticuspidal semigroup property -- 6. The P-anticuspidal operator J[sub(P,Γρp,)] and the conjectured spectral expansion -- 7. Onward -- Appendix. The Heat Kernel -- 1. Dodziuk's uniqueness theorem -- 2. The fundamental solution and the heat kernel -- 3. Properties of the heat kernel -- 4. Compact manifolds -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.