Báo cáo toán học: "Counting distinct zeros of the Riemann zeta-function" docx

... 13, 1994. Abstract. Bounds on the number of simple zeros of the derivatives of a function are used to give bounds on the number of distinct zeros of the function. The Riemann ξ-function is defined ... generically, the left side of (7) equals N (j) s (T ). In other words, the zeros of the derivatives of a generic function are all simple, except for thos...

Ngày tải lên: 07/08/2014, 06:20

... me to the area of log-concave sequences. Abstract We provide a combinatorial proof for the fact that for any fixed n, the sequence {i(n, k )} 0≤k ≤ ( n 2 ) of the numbers of permutations of length ... i(p) of inversions, and the study of numbers i(n, k)ofn-permutations having k inversions, is a classic area of combinatorics. The best-known result is the following [4...

Ngày tải lên: 07/08/2014, 08:22

... − 2 3  2π 2 − 46 3  . The fourth derivative of the HC on the argument n, and the common radius is of the form Figure 8 The HC and its derivative with the HC maximum location and optimum for the value of the degree ... 2)  . In general, the HC of the mth derivative of n can be defined on the basis of the pro- duct of polygamma (psi) polynomial of t...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 09:46

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Ngày tải lên: 05/08/2014, 15:21

... n)-generated group. The motivation for this question came from the calculation of the genus of finite simple groups [26]. It can be shown that the problem of finding the genus of a finite simple group ... done while the authors were on a sabbatical lea ve. The first author expresses his thanks for the hospitality and facilities provided by the Department of Mathematics...

Ngày tải lên: 06/08/2014, 04:21

... subset of [d] × [d](where[d]isdefinedtobe{1, 2, ,d})andtherook numbers r B k of a board are the number of subsets of B of size k such that no two elements have the same first coordinate or the same ... ···(x−n+1). Then we have the following reciprocity theorem. Theorem. For any board B ⊂ [d] × [d], R(B; x)=(−1) d R(B; − x − 1). The existing proofs derive this as a corollary...

Ngày tải lên: 07/08/2014, 06:20

... 2. Thus, the conjecture states that there exists an integer K such that, for all k ≥ K, L k (G) possesses the MDGP. The focus of this paper is to present a proof of this conjecture. In the following ... of k gener- ates a component of k+1 for k ≥ J 1 , and every component of k+1 is generated by exactly one component of k . Proof. Let c k denote the number of components...

Ngày tải lên: 07/08/2014, 06:20