✦ LIBER ✦

A Proof of a Conjecture of C.L. Siegel

✍ Scribed by J.T. Ding

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 243 KB
Volume: 46
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1994.1001

No coin nor oath required. For personal study only.

✦ Synopsis

Let (M_{n}) be the Minkowski fundamental domain for the space of (n \times n) real, symmetric, and positive definite matrices under the action of the unimodular group (S L_{n}(Z)). C. L. Siegel conjectured that (d(A, B)-f(A, B) \leqslant C(n)), for (A, B \in M_{n}), where (d) and (f) are the geodesic and the reduced geodesic distances, respectively, and (C(n)) is a constant depending only on (n). This conjecture appears in his book ("Zur Reduktionstheorie Quadratischer Formen," The Mathematical Society of Japan, 1959). By reducing the problem to the diagonal matrices in (M_{n}), we obtain a proof. 1994 Academic Press, Inc

📜 SIMILAR VOLUMES

Proof of a conjecture of nirenberg

✍ Robert Osserman 📂 Article 📅 1959 🏛 John Wiley and Sons 🌐 English ⚖ 209 KB 👁 1 views

Proof of a Chromatic Polynomial Conjectu

Proof of a Chromatic Polynomial Conjecture

✍ F.M. Dong 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 138 KB

Let P(G, \*) denote the chromatic polynomial of a graph G. It is proved in this paper that for every connected graph G of order n and real number \* n, (\*&2) n&1 P(G, \*)&\*(\*&1) n&2 P(G, \*&1) 0. By this result, the following conjecture proposed by Bartels and Welsh is proved: P(G, n)(P(G, n&1))

A Simple Proof of a Conjecture of Simion

✍ Yi Wang 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 73 KB

Simion had a unimodality conjecture concerning the number of lattice paths in a rectangular grid with the Ferrers diagram of a partition removed. Hildebrand recently showed the stronger result that these numbers are log concave. Here we present a simple proof of Hildebrand's result.

A New Proof of a Conjecture of Antoniadi

A New Proof of a Conjecture of Antoniadis

✍ Zhenfu Cao; Shanzhi Mu; Xiaolei Dong 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 96 KB

We give a new and elementary proof that the equation x 3 &1=31y 2 has only the integral solutions (x, y)=(1, 0), (5, 2), (5, &2).

Proof of a conjecture of Alan Hartman

✍ Liu, Q. Z.; Yap, H. P. 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 265 KB 👁 2 views

A tree T is said to be bad, if it is the vertex-disjoint union of two stars plus an edge joining the center of the first star to an end-vertex of the second star. A tree T is good, if it is not bad. In this article, we prove a conjecture of Alan Hartman that, for any spanning tree T of K 2m , where

Proof of a conjecture on game domination

✍ O. Favaron; H. Karami; R. Khoeilar; S. M. Sheikholeslami; L. Volkmann 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 87 KB 👁 1 views

## Abstract The game domination number of a (simple, undirected) graph is defined by the following game. Two players, \documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}${\mathcal{A}}$\end{document} and \docume