Titlebook: Number Theory and Discrete Mathematics; A. K. Agarwal,Bruce C. Berndt,Michel Waldschmidt Book 2002 Hindustan Book Agency (India) 2002

intricacy

职业拳击手

真实的你

,Integrity of , × ,The vertex Integrity, .(.), of a graph . is defined as. where .(. − .) is the order of the largest component of . − .. In this paper, we compute .(. × .), the vertex integrity of the Cartesian product of . and ..

自恋

幻影

Transcendental Infinite Sums and Some Related Questions,Erdős and Chowla put forward some questions regarding non-vanishing of certain infinite sums. In this article, we present an expository account of results obtained in that direction. These include some interesting results of Baker, Birch and Wirsing and some recent work of the present author jointly with Saradha, Shorey and Tijdeman.

grounded

NOT

The Problems Solved by Ramanujan in the Journal of the Indian Mathematical Society,Between 1912 and 1914, eight solutions by Ramanujan to questions posed in the . were published. Since these solutions have not heretofore appeared elsewhere, and since some of these problems evidently motivated certain entries in his notebooks [6], in this paper, we present all eight problems and solutions and provide some commentary on them.

Reverie

vasospasm

Multiple Polylogarithms: An Introduction,this is the classical polylogarithm Li. (.). These multiple polylogarithms can be defined also in terms of iterated Chen integrals and satisfy .. Multiple polylogarithms in several variables are defined for . ≥ 1 and |.| < 1(1 ≤ . ≤ .) by., and they satisfy not only shuffle relations, but also .. Wh

cruise

A (Conjectural) 1/3-phenomenon for the Number of Rhombus Tilings of a Hexagon which Contain a Fixedth side lengths 2. + ., 2. + ., 2. + ., 2. + ., 2. + ., 2. + . contains the (horizontal) rhombus with coordinates (2. + ., 2. + .) is equal to ., where .(.) is a rational function in .. Several specific instances of this “1/3-phenomenon” are made explicit.