Arithmetical Properties of Elliptic Bernoulli and Euler Numbers
نویسندگان
چکیده
We introduce elliptic analogues to the Bernoulli ( resp. Euler) numbers and functions. The first aim of this paper is to state and prove that our elliptic Bernoulli and Euler functions satisfied Raabe’s formulas (cf. Theorems 3.1.1, 3.2.1). We define two kinds of elliptic Dedekind-Rademacher sums, in terms of values of our elliptic Bernoulli (resp. Euler) functions. The second aim of this paper is to state and prove a Dedekind reciprocity Law for our elliptic Dedekind-Rademacher sums (cf.Theorems 4.3.1, 4.4.1). Our results recover the well known classical results.
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