Đề tài " The Hasse principle for pairs of diagonal cubic forms " doc

... write M s (p h ) for the number of solutions of the system (1.1) with x ∈ (Z/p h Z) s . THE HASSE PRINCIPLE FOR PAIRS OF DIAGONAL CUBIC FORMS 889 Lemma 12. Suppose that the linear forms L 1 (θ) ... derive an upper THE HASSE PRINCIPLE FOR PAIRS OF DIAGONAL CUBIC FORMS 877 bound of the shape (4.5), subject to the constraints (4.4), wherein...

Ngày tải lên: 22/03/2014, 20:21

... case of Maass forms; 1 this estimate together with the Burgess bound (to handle the contribution from the continuous spectrum) is sufficient to finish the proof of Theorem 2. Remark 1.5. We find rather ... handle the shifted convolutions sums (1.5). The proof of Theorem 3 in a more general form is given in Section 6. In the appendix we provide a proof of a subconvexity bou...

Ngày tải lên: 22/03/2014, 16:20

... +2)+O(1))} so that the lower bound in the corollary follows with v + = w − ky for some 1 ≤ k ≤ [w/y]. The proof of the upper bound in the corollary is similar. We now embark on the proof of Theorem 3.1. ... consider now the problem of providing a better localization of the sign changes of E for small values of u. Our main result of this section is the follo...

Ngày tải lên: 16/02/2014, 06:20

... (n, n 2 ). Proof. The proof is by induction. The result for Q 0 is obvious, and the result for Q 1 ∼ = P 1 is Property (D). Except for the base cases in the previous paragraph, the argument for the odd ... sum of the outer terms. The right term provides a generator of degree (2n, n), and the left term provides the rest of the generators. The above proof...

Ngày tải lên: 06/03/2014, 08:21

... and on this subspace the formula for the dual action of G is the same (this was used in the proof of Corollary 3.10). Recall that βG (the Stone- ˇ Cech compactification of the discrete group G) can ... xyx −1 (see the proof of THE DERIVATION PROBLEM FOR GROUP ALGEBRAS 225 Corollary 1.2), they write N for the closure of the elements of G belonging to relativ...

Ngày tải lên: 06/03/2014, 08:21

... proof of Theorem 1. (ii) Actually the above results show how one can read off the covering properties of the family of intervals I i,j (µ) for i<jfrom the corresponding overlappings of the ... important to keep track of exactly how the parts of the J + i ∩ J − j ’s are placed to cover G(µ) and J(µ). This has been more or less analysed in the above proof except...

Ngày tải lên: 14/03/2014, 22:20

... eventually the initial path of length N of C k , then eventually the initial path of length N of A k is the initial path of length N of BC. Eventually, the terminal path of length N of A k is the terminal ... sequence of paths in G, then either {A k } is constant or, for all N, the initial and terminal paths of A k of length N are eventually constant. Proof...

Ngày tải lên: 22/03/2014, 20:20

... Z p ) × , E F is the closure of the projec- tion of the global units O × F into U F , and C F is the closure of the projection of the subgroup of elliptic units (as defined for example in §1 of [Ru3]) ... denote the formal group giving the kernel of reduction modulo p on E. The theory of complex multiplication shows that ˆ E is a Lubin-Tate formal group of...

Ngày tải lên: 28/03/2014, 22:20

... completes the proof of the claim, and the proof of the lemma. The next proposition gives the global estimate for the level set of the constrained sharp fractional maximal function of u. Proposition ... lower bounds will be specified for k. These bounds are required for the proof to work, and depend only on C and α. To realize the contradiction at the end of...

Ngày tải lên: 29/03/2014, 07:20

... influence on the types of any of the other particles during [0,s] (and of course no influence on the paths of these other particles), as long as we stay on I 1 ∩I 2 (compare the argument for (2.36) ... most of the estimates for the terms in the right-hand side here for k ≥ 2. The basic inequalities remain valid for k = 1 by trivial modifications which we again l...

Ngày tải lên: 16/02/2014, 06:20