1549380232-Automorphic_Forms_and_Applications__Sarnak_

CONSTANT TERMS. THE BASIC ESTIMATE 27 mk varies in a relatively compact set as x E 6. There exists therefore c > 0 such tha ...

28 ARMAND BOREL, AUTOMORPHIC FORMS ON REDUCTIVE GROUPS proper parabolic Q-subgroups containing P are zero. Let nqf = fq. This is ...

CONVOLUTION OPERATORS ON CUSPIDAL FUNCTIONS 29 7.3. Lemma. Let Z be a locally compact space with a positive measure μ such tha ...

30 ARMAND BOREL, AUTOMORPHIC FORMS ON REDUCTIVE GROUPS is fast decreasing for every D E U(g).) It is endowed with the seminorms ...

AUTOMORPHIC FORMS AND THE REGULAR REPRESENTATION ON r\G 31 supported functions by the rule: (83) 7r(a)v = [ a(x)n(x)vdx (v EV) ...

32 ARMAND BOREL, AUTOMORPHIC FORMS ON REDUCTIVE GROUPS Lemma, Z(g) operates by homotheties. Therefore, every element of VJ( is Z ...

SOME ESTIMATES OF GROWTH FUNCTIONS 33 is well-defined. f and g are said to be orthogonal if (!, g) = 0. 10.2. Let f E C';:mg a ...

34 ARMAND BOREL, AUTOMORPHIC FORMS ON REDUCTIVE GROUPS the parabolic subgroup PJ, where J is the set of o: for which ma = 0. We ...

EISENSTEIN SERIES 35 Proof. Let w EC. By t he proposition (93) a(dx)w--< a(d)wa(x)w (d E D , x E 6). Since Dis compact, a(d ...

36 ARMAND BOREL, AUTOMORPHIC FORMS ON REDUCTIVE GROUPS C. The map which associates to >. E X(A)c its differential at 1 is an ...

EISENSTEIN SERIES 37 we may as well assumes to be real (i.e. in X(A)). If x varies in a compact set D then, by Section 5.7, th ...

38 ARMAND BOREL, AUTOMORPHIC FORMS ON REDUCTIVE GROUPS (101) now follows with t = t1 + :Z.:::iEI μi. D 12.7. Conclusion of the p ...

BIBLIOGRAPHY l. A. Borel, (a) Linear algebraic groups, (b) Reductive groups, ( c) Introduction to automorphic forms, Proc. Symp. ...

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Spectral Theory of Automorphic Forms L. Clozel ...

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!AS/Park City Mathematics Series Volume 12, 2002 Spectral Theory of Automorphic Forms L. Clozel Foreword Assume G is a semi-simp ...

44 L. CLOZEL, SPECTRAL THEORY OF AUTOMORPHIC FORMS those for a subgroup H, supposed better known. This is explained, with proofs ...

FOREWORD 45 As informal is my use of the word "Conjecture": if Conjecture 1 is unimpeach- able, my formulation of Conjecture 2, ...

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