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....

Connecting a physiological model to a cognitive architecture presents an attractive option to better simulate a wide range of human behavior. This connection should facilitate both the effects of physiology on cognition (e.g. hunger and decision-making), and the effects of cognition on physiology (e.g. autonomic responses to memory featuring particularly aversive stimuli). To add physiology to ...

The article presents an algorithm to compute a C[t]-module basis G for a given subalgebra A over a polynomial ring R = C[x] with a Euclidean domain C as the domain of coefficients and t a given element of A. The reduction modulo G allows a subalgebra membership test. The algorithm also works for more general rings R, in particular for a ring R ⊂ C((q)) with the property that f ∈ R is zero if an...

Let E be an elliptic curve having Complex Multiplication by the ring OK of integers of K = Q( √−D), let H = K(j(E)) be the Hilbert class field of K. Then the Mordell-Weil group E(H) is an OK-module. Its Steinitz class St(E) is studied here. In particular, when D is a prime number, St(E) is determined: If D ≡ 3 (mod 4) then St(E) = 1; if D ≡ 1 (mod 4) then St(E) = [P]t, where P is any prime-idea...

‎in this paper, we study some kinds of majorizations on $textbf{m}_{n}$ and their linear or strong linear preservers. also, we find the structure of linear or strong linear preservers which are multiplicative, i.e.  linear or strong linear preservers like $phi $ with the property $phi (ab)=phi (a)phi (b)$ for every $a,bin textbf{m}_{n}$.

Let E be an elliptic curve having Complex Multiplication by the full ring OK of integers of K = Q( √ −D), let H = K(j(E)) be the Hilbert class field of K. Then the Mordell-Weil group E(H) is an OK-module, and its Steinitz class St(E) is studied. When D is a prime number, it is proved that St(E) = 1 if D ≡ 3 (mod 4); and St(E) = [P]t if p ≡ 1 (mod 4), where [P] is the ideal class of K represente...

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...

Some results are obtained on the group of rational points on elliptic curves over infinite algebraic number fields. A certain naturally defined class of Dedekind domains, elliptic Dedekind domains, are described and it is shown that every countable abelian group can be realized as the class group of an elliptic Dedekind domain. Introduction. Let E be an elliptic curve defined over a field K. Le...

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...