Đề tài " The number of extensions of a number field with fixed degree and bounded discriminant " docx

... (This data was obtained with the commands InvariantRing, PrimaryInvariants, and SecondaryInvariants in Magma.) One checks that R = R/f 1 R is an integral domain. Let S be the subring of R generated ... field with fixed degree and bounded discriminant By Jordan S. Ellenberg and Akshay Venkatesh* Abstract We give an upper bound on the number of extensions of a fix...

Ngày tải lên: 06/03/2014, 08:21

... Achlioptas and Assaf Naor Annals of Mathematics, 162 (2005), 1335–1351 The two possible values of the chromatic number of a random graph By Dimitris Achlioptas and Assaf Naor* Abstract Given ... 63–70. [2] N. Alon and M. Krivelevich, The concentration of the chromatic number of random graphs, Combinatorica 17 (1997), 303–313. THE CHROMATIC NUMBER OF A...

Ngày tải lên: 29/03/2014, 07:20

... together with the global graph constraints. The result is exactly the µ summand in (1.7) (the edge and graph automorphisms 574 A. OKOUNKOV AND R. PANDHARIPANDE are incorporated in the prefactors). ... taking, instead of {ψ k } and {ψ ∗ k }, any linear basis of the space V of creation operators and the cor- responding dual basis of the space of annihilation...

Ngày tải lên: 16/02/2014, 06:20

... call them the constant and linear part of t, respectively. If the linear part of t vanishes, then the quadratic part of t u , which is a quadratic map TE z → R, is again independent of u. We then ... whose composition with u is the germ at 0 of a polynomial function t u of degree ≤ k on the vector space TE z . The constant part (a real number) and the l...

Ngày tải lên: 06/03/2014, 08:21

... over a perfect field By Kazuya Kato and Takeshi Saito Abstract For an -adic sheaf on a variety of arbitrary dimension over a perfect field, we define the Swan class measuring the wild ramification as ... product and alteration (Theorem 3.2.3). The aim of this paper is to show that the map (0.1) gives generalizations to an arbitrary dimension of the classical invariants...

Ngày tải lên: 06/03/2014, 08:21

... γ ε j ,3 separate Σ ε j ,1 and σ 2 . The next lemma bounds the area of a minimal surface with two sides and an interior boundary in a small ball in terms of the length of the sides, provided that the ... function of s, a standard argument then gives (II.1.16). Annals of Mathematics The space of embedded minimal surfaces of fixed genus in a 3-man...

Ngày tải lên: 14/02/2014, 17:20

... Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. Finally, the author acknowledges the referee for a thorough reading of the paper and for helpful suggestions. This work was partially ... lie all above their expected values. An analogy from probability theory is to ask for the likelihood that a random walk on the real numbers, with each step ha...

Ngày tải lên: 06/03/2014, 08:21

... of the set of points of large curvature – the axis of the double spiral staircase. The reader may find it useful to also look at the survey [CM8] and the expository article [CM9] for an outline of ... results, and their proofs, and how these results fit together. The article [CM9] is the best to start with. *The first author was partially supported by NSF Gran...

Ngày tải lên: 14/03/2014, 22:20