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Numbers of Solutions of Congruences and Rationality of Generating Functions

✍ Scribed by Han Qing

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 171 KB
Volume: 5
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1999.0247

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📜 SIMILAR VOLUMES

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Let R, represent the set of all rational numbers which are integral (mod m ) . We recall that a/b is integral (mod m) if m and b are relatively prime. If {a,L} is a sequence of numbers in R,, where p is a fixed rational prime, it is customary to say that a, satisfies KUMMER'S congruence when for al

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In this paper, we find simple 2-adic congruences mod 2 [nÂ2]+1 for the No rlund numbers B (n) n and for the Bernoulli numbers of the second kind b n . These congruences improve F. T. Howard's mod 8 congruences (in ``Applications of Fibonacci Numbers, '' Vol. 5, pp. 355 366, Kluwer Academic, Dordrech

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Some Families of Generating Functions Associated with the Stirling Numbers of the Second Kind

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## Introduction. That every integrally closed subring of the field of algebraic numbers is a ring of quotients of its subring of algebraic integers is a remark of 131. The purpose of the present note is to prove this assertion without the hypothesis of integral closure (Theorem A). The proof rests

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✍ Ernst-Ulrich Gekeler 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 133 KB

We prove congruences of shape E kþh E k Á E h ðmod NÞ modulo powers N of small prime numbers p; thereby refining the well-known Kummer-type congruences modulo these p of the normalized Eisenstein series E k : The method uses Serre's theory of Iwasawa functions and p-adic Eisenstein series; it presen