✦ LIBER ✦

Multiplicative Relations in Powers of Euler's Product

✍ Scribed by Scott Ahlgren

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 133 KB
Volume: 89
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2648

No coin nor oath required. For personal study only.

✦ Synopsis

In a recent paper, Cooper, Hirschhorn, and Lewis conjecture many relations among the coefficients of certain products of powers of Euler's product. Here we use the theory of modular forms with complex multiplication to prove these conjectures.

📜 SIMILAR VOLUMES

Functions, Functional Relations, and the

Functions, Functional Relations, and the Laws of Continuity in Euler

✍ Giovanni Ferraro 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 132 KB

La nozione euleriana di funzione presenta un duplice aspetto: essa era, a un tempo, relazione funzionale tra quantità e formula composta da simboli operazionali, da costanti, e da variabili. Queste ultime erano concepite come universali e pertanto godenti di particolari proprietà. Anche se il calcol

Power Relations and Group Aggregation in

Power Relations and Group Aggregation in the Multiplicative AHP and SMART

✍ J. BARZILAI; F. A. LOOTSMA 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 178 KB 👁 1 views

The relative power of the members in a group of decision makers can be incorporated in the Multiplicative AHP via power coefficients in the logarithmic least squares whereby we analyse the pairwise comparison matrices. When each decision maker judges every pair of alternatives under each of the crit

Acquisition of synonyms using relations

Acquisition of synonyms using relations in product specification tables

✍ Tsunehito Seki; Kazutaka Shimada; Tsutomu Endo 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 739 KB

## Abstract In this paper, we propose a method for acquisition of synonyms from product specifications. Product specifications are presented in tabular form. We utilize structure information, such as attribute‐value pairs, for the acquisition process. First, we extract target words from attributes

Computation of Euler’s type sums of the

Computation of Euler’s type sums of the products of Bernoulli numbers

✍ Aleksandar Petojević; H.M. Srivastava 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 386 KB

In this work, the authors present several formulas which compute the following Euler's type and Dilcher's type sums of the products of Bernoulli numbers B n : respectively, where denotes, as usual, the multinomial coefficient.

Induced ordered weighted geometric opera

Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations

✍ F. Chiclana; E. Herrera-Viedma; F. Herrera; S. Alonso 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 163 KB

In this article, we introduce the induced ordered weighted geometric (IOWG) operator and its properties. This is a more general type of OWG operator, which is based on the induced ordered weighted averaging (IOWA) operator. We provide some IOWG operators to aggregate multiplicative preference relati

Multiplicative versions of Klyachko’s th

Multiplicative versions of Klyachko’s theorem in finite factors

✍ Tetsuo Harada 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 131 KB