Corrigenda to: ‘‘Generalized Euler and class numbers ‘‘
نویسندگان
چکیده
منابع مشابه
Arithmetic Properties of Generalized Euler Numbers
The generalized Euler number En|k counts the number of permutations of {1, 2, . . . , n} which have a descent in position m if and only if m is divisible by k. The classical Euler numbers are the special case when k = 2. In this paper, we study divisibility properties of a q-analog of En|k. In particular, we generalize two theorems of Andrews and Gessel [3] about factors of the q-tangent numbers.
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New enumerating functions for the Euler numbers are considered. Several of the relevant generating functions appear in connection to entries in Ramanujan’s Lost Notebook. The results presented here are, in part, a response to a conjecture made by M. E. H. Ismail and C. Zhang about the symmetry of polynomials in Ramanujan’s expansion for a generalization of the Rogers-Ramanujan series. Related g...
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In this paper, concepts of the generalized Bernoulli and Euler numbers and polynomials are introduced, and some relationships between them are established.
متن کاملA Note on the Generalized Euler Numbers and Polynomials
Let p be an odd prime number. Throughout this paper Zp, Qp, C, and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field, and the completion of algebraic closure of Qp. The normalized valuation in Cp is denoted by | · |p with |p|p = 1 p . We say that f is a uniformly differentiable function at a point a ∈ Zp and denote...
متن کاملClass Numbers and a Generalized Fermat Theorem
The purpose of this paper is twofold. In the first section we provide sufficient conditions for the divisibility of the class number of certain algebraic number fields by prime powers and applications thereof. We were initially inspired in this regard by Watabe [ 111, wherein some of the results are false thereby leading to the above. In the second section we generalize Fermat’s well-known “two...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1968
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1968-0227093-9