Đề tài " The local converse theorem for SO(2n+1) and applications " potx

... GL n−1 (k) × SO 3 (k), and unipo- Annals of Mathematics The local converse theorem for SO(2n+1) and applications By Dihua Jiang and David Soudry* THE LOCAL CONVERSE THEOREM 761 tent ... by the local gamma factors and their twisted versions. Such acharacterization is traditionally called the Local Converse Theorem, and is the local anal...

Ngày tải lên: 22/03/2014, 15:21

... that the set {Y ∈ M : τ(Y ) ≤ τ (X)} has the form (∗). Since this is true for every X ∈ M, in fact all of M must have the form (∗). 3. The fundamental theorem 3.1. Theorem. For 0 < α < 1, there ... WHITE The conclusions then follow immediately from Theorems 2.6 and 3.1. (See also the remark after Theorem 3.1.) Remark. These theorems remain true (with essentially...

Ngày tải lên: 06/03/2014, 08:21

... Proposition 2.1. On the bright side, it suffices to know these only for u, and therefore to have a less restrictive condition for v. Proof. We prove the result here for the case n ≥ 3. The case n =2is considerably ... solution in the sense of distribu- tions, yielding the existence part of (WP1). The conditions (WP3) and (WP4) hold for u since they hold uniformly for...

Ngày tải lên: 15/03/2014, 09:20

... 0 and at x =0 by mf and sf, the ‘main face’ and the ‘side face’, respectively, and we denote the corner mf ∩sf by K.Thusmf=X × X ◦ ,sf=∂X × X ◦ × R  0 and K = ∂X × X ◦ . We shall see that the ... s(1 − sk)Ξ i ∂ Ξ i . The vector field W = V/s is tangent to  sf and transverse to the front face in the region of validity of these coordinates. The calculation for th...

Ngày tải lên: 15/03/2014, 09:20

... X + ,(4.6) for η ∈ a ∗ q sufficiently antidominant, so that the function is independent of η. The following theorem represents the main step in the proof of the Paley- Wiener theorem. Theorem 4.4. ... holds for all φ ∈O 1 . The statement (ii) follows immediately from the above and the corre- sponding statement in Lemma 7.1. 8. Proof of Theorem 4.4 The inversion fo...

Ngày tải lên: 22/03/2014, 20:20

... disjoint and satisfy the cone property (1) and, therefore, we get a bound for the sum of the radii s i of these balls  i s i ≤ C 0 R/c in .(2.33) Combining this with the chord arc property (5) then ... (4) together with the fact that the points y i go from top to bottom by (2) and (3). Second, (1) and (5) imply a bound for the diameter of the union of the balls B...

Ngày tải lên: 29/03/2014, 07:20

... is not conformal, for in the conformal case the left-hand side is 1 and the inequality is obvious. Let Rs be the direction most contracted by L, and let θ, φ ∈ [0,π] be the angles that the directions Rv ... R d still form an atlas of M. The latter will be denoted A. Let A ∗ and A be fixed once and for all. By compactness, there exists r 0 > 0 such that for each x...

Ngày tải lên: 06/03/2014, 08:21

... ·  G Z \G 1 R dg = 6π 3 n i · X 6 · ζ(2) π · ζ(2)ζ(3) 2π 2 = ζ(2) 2 ζ(3) 2n i X, proving Theorem 7. 3. Pairs of ternary quadratic forms and Theorems 1–5 Theorem 6 and Theorem 7 together now immediately imply the following Theorem 22. Let M ∗(i) 4 (ξ,η) denote the number ... completes the proof. Proof of Theorem 2. We first prove the analogue of Theorem 2 for the se...

Ngày tải lên: 22/03/2014, 20:20

... Jong for pointing out an error in the proof of Theorem 1.1 in the first version of the article, and the referee for forcing and helping us to restore the whole strength of Theorem 1.1 in the corrected ... comments and remarks 5.1. Theorem 1.5 ii) is formulated for N 1 and not for the higher coniveau levels N κ of ´etale cohomology. The appendix to this art...

Ngày tải lên: 22/03/2014, 20:20

... π v )isholomorphic and nonzero for s ≥ 1 2 . The claim follows. Hence L( 3 2 ,π) > 0, and therefore, L( 1 2 ,π) > 0. It remains to prove (4). The operator (π, s) and the form (π, s) admit alocal analogue ... ∈ Irr n and σ ∈ Irr(S m ) then π σ =Σ n (π  σ)inthe Grothendieck group since π ⊗ σ and Σ n (π  ⊗ σ) are associate. The case k>1 and the last statement a...

Ngày tải lên: 22/03/2014, 15:21