1549380232-Automorphic_Forms_and_Applications__Sarnak_
Lecture 5. Some applications of subconvexity In this last section, we describe several applications of subconvex bounds in arith ...
268 PH. MICHEL, ANALYTIC NUMBER THEORY AND FAMILIES OF £ -FUNCTIONS One chooses V a smooth non-negative function compactly suppo ...
LECTURE 5. SOME APPLICATIONS OF SUBCONVEXITY 269 5.2. Subconvexity vs. Minkowski Let K be an imaginary quadratic field. We denot ...
270 PH. MICHEL, ANALYrIC NUMBER THEORY AND FAMILIES OF £-FUNCTIONS is cyclic.) One may then look for an ideal a generating G of ...
LECTURE 5. SOME APPLICATIONS OF SUBCONVEXITY 271 in terms of the class number h( -n) of primitive positive binary quadratic form ...
272 PH. MICHEL, ANALYTIC NUMBER THEORY AND FAMILIES OF £ -FUNCTIONS is in fact a holomorphic modular form of weight l = k + 3/2 ...
LECTURE 5. SOME APPLICATIONS OF SUBCONVEXITY 273 and in particular by Deligne's bound for holomorphic cusp forms Cl.A 9 (n)I ~ T ...
274 PH. MICHEL, ANALYTIC NUMBER THEORY AND FAMILIES OF £-FUNCTIONS On the other hand, if q is inert in K, then the reduction ma ...
LECTURE 5. SOME APPLICATIONS OF SUBCONVEXITY where W ( 'ljJ, V) denotes the "twisted" Weyl sum 1 W('l/;, V) = IPic(OK)I L ~(cr)V ...
276 PH. MICHEL, ANALYTIC NUMBER THEORY AND FAMILIES OF £ -FUNCTIONS for e, e' E a gss (F q ) , so that M^0 is the orthogonal com ...
LECTURE S. SOME APPLICATIONS OF SUBCONVEXITY 277 ordered in increasing size: i.e. 6.cpj + Aj'Pj = 0 with 0 = >.. 0 ~ >.. 1 ...
278 PH. MICHEL, ANALYTIC NUMBER THEORY AND FAMILIES OF L -FUNCTIONS weak-* converges on X 0 (q)(C ) to the normalized Poincare m ...
LECTURE 5. SOME APPLICATIONS OF SUBCONVEXITY 279 which follows from the Hadamard/ de la Vallee-Poussin zero-free region. For V = ...
280 PH. MICHEL, ANALYTIC NUMBER THEORY AND FAMILIES OF L-FUNCTIONS By Stirling's formula, one has { E 00 (z, 1 /2 + i t)dμ1(z) « ...
LECTURE 5. SOME APPLICATIONS OF SUBCONVEXITY 281 have been given for G L 3 [BFG], but so far they seem difficult to use effectiv ...
282 PH. MICHEL, ANALYTIC NUMBER THEORY AND FAMILIES OF L-FUNCTIONS Proof. By ( 4.25), Stirling's formula, and the value of the f ...
LECTURE 5. SOME APPLICATIONS OF SUBCONVEXI'IY 283 When q is squarefree at least, one can check that this conjecture follows from ...
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[A] [AB] [AC] [AL] [ALi] [Ar] [AU] [Ban] [Bar] [BR] [BM] [BDl] [BD2] [BD3] [BR] Bibliography Arenas, A. An arithmetic problem on ...
286 [BR2] [BR3] [Bo] [BFil] [BFI2] [BFI3] [BS] [BSSP] [BL] [BCDT] [BH] [Bu] [BFG] [CMP] [Col] [Co2] [CoPS] [CoPSS] [ClU] [C-V] [ ...
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