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...

In the absence of the axiom of choice there are several possible nonequivalent ways of translating the intuitive idea of “infinity” into a mathematical definition. In [10], Tarski investigated some natural infinity notions notions, and his research was continued by Levy [8], Truss [12], Spǐsiak and Vojtas [9], Howard and Yorke [4] and others. The most prominent definitions of finiteness are the...

S (in alphabetic order by speaker surname) Speaker: Abdelmejid Bayad (Université d’Evry Val d’Essonne) Title: Some facets of multiple Dedekind-Rademacher sums Abstract: We introduce two kind of multiple Dedekind-Rademacher sums, in terms of Bernoulli and Jacobi modular forms. We prove their reciprocity Laws, we establish the Hecke action on these sums and we obtain new Knopp–Petersson identies....

Richard Dedekind's characterization of the real numbers as the system of cuts of rational numbers is by now the standard in almost every mathematical book on analysis or number theory. In the philosophy of mathematics Dedekind is given credit for this achievement, but his more general views are discussed very rarely and only superrcially. For example, Leo Corry, who dedicates a whole chapter of...

For certain classes of Prüfer domains A, we study the completion Â,T ofA with respect to the supremum topology T = sup{Tw|w ∈ Ω}, where Ω is the family of nontrivial valuations on the quotient field which are nonnegative on A and Tw is a topology induced by a valuation w ∈ Ω. It is shown that the concepts ‘SFT Prüfer domain’ and ‘generalized Dedekind domain’ are the same. We show that if E is t...

A bipartite monoid is a commutative monoid Q together with an identified subset P ⊂ Q. In this paper we study a class of bipartite monoids, known as misère quotients, that are naturally associated to impartial combinatorial games. We introduce a structure theory for misère quotients with |P| = 2, and give a complete classification of all such quotients up to isomorphism. One consequence is that...

Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness sharp elements. Being apart is positive formulation being unequal, similar to how inhabitedness nonemptiness. To exemplify sharpness, note that lower real if only it located. first main result for large class dcpos, Bridges-Vita topol...

In this paper, we study Dedekind sums and we connect them to the mean values of Dirichlet L-functions. For this, we introduce and investigate higher order dimensional Dedekind-Rademacher sums given by the expression Sd( −→ a0 , −→ m0) = 1 a0 0 a0−1 ∑