Jorgenson J. Heat Eisenstein series on SLn(C) / Jorgenson J., Lang S. - Providence: American Mathematical Society, 2009. - viii, 127 p.: ill. - (Memoirs of the American Mathematical Society; Vol.201, N 946 (end of volume)). - Bibliogr.: p.119-121. - Ind.: p.123-127. - ISBN 978-0-8218-4044-3  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Contents

Contents ........................................................ v Acknowledgements ............................................. viii Introduction .................................................... 1 Notation and Terminology ........................................ 5 Chapter 1 Estimates on SLn Parabolics 1 The hermitian norm on SLn and Siegel sets .................... 9 2 Volume and lattice point estimates .......................... 16 3 Estimates of A-projections .................................. 20 4 Standard reduced parabolics ................................. 23 5 Characters on parabolics .................................... 29 6 Estimates of Aρ-projections ................................. 33 7 Parabolic integral formulas ................................. 35 Chapter 2 Eisenstein Series 1 The character Eisenstein series ............................. 41 2 Twists of character Eisenstein series ....................... 46 3 Two-character Eisenstein series ............................. 51 4 The Gauss space ............................................. 53 5 The parabolic Eisenstein integration formula ................ 58 Chapter 3 Adjointness and Inversion Relations 1 Adjointness formulas and F-cuspidality ...................... 61 2 Adjointness and initial conditions formulas ................. 70 3 P-cuspidality and heat Eisenstein series .................... 72 4 The family of anticuspidal operators JP,Г,ε,t ................. 80 Chapter 4 Applications of the Heat Equation 1 Parabolics and the (a, n)-characters ........................ 85 2 Direct image of Casimir on parabolics ....................... 87 3 The differential equation for ЈP,Г,K and EP,K# ................ 91 4 Convolution of TrГ(Kx) and the Eisenstein series ...................................................... 95 5 The P-anticuspidal semigroup property ....................... 96 6 The P-anticuspidal operator JpPГ,Pρ and the conjectured spectral expansion ......................................... 100 7 Onward ..................................................... 104 Chapter Appendix. The Heat Kernel 1 Dodziuk's uniqueness theorem ............................... 107 2 The fundamental solution and the heat kernel ............... 109 3 Properties of the heat kernel .............................. 113 4 Compact manifolds .......................................... 114 Bibliography .................................................. 119 Index ......................................................... 123