Let $k$ be a global field, let $A$ Dedekind domain with $\text{Quot}(A) = k$, and $K$ finitely generated field. Using unified approach for both elliptic curves Drinfeld modules $M$ defined over having trivial endomorphism ring, $k= \mathbb{Q}$, $A \mathbb{Z}$ in the former case function its ring of functions regular away from fixed prime latter case, any nonzero ideal $\mathfrak{a} \lhd A$ we p...

Using Weil’s explicit formula, we propose a method to compute low zeros of the Dedekind zeta function. As an application of this method, we compute the first zero of the Dedekind zeta function associated to totally complex fields of degree less than or equal to 30 having the smallest known discriminant.

The concepts of closure systems and closure operations in lattice theory are basic and applied to many fields in mathematics and theoretical computer science. In this paper authors find out a suitable definition of closure systems in Dedekind categories, and thereby give an equivalence proof for closure systems and closure operations in Dedekind categories.

A module is called uniseriat if it has a unique composition series of finite length. A ring (always with 1) is called serial if its right and left free modules are direct sums of uniserial modules. Nakayama, who called these rings generalized uniserial rings, proved [21, Theorem 171 that every finitely generated module over a serial ring is a direct sum of uniserial modules. In section one we g...

We investigate the modular group as a finitely presented group. It has a large collection of interesting quotients. In 1987 Conder substantially identified the onerelator quotients of the modular group which are defined using representatives of the 300 inequivalent extra relators with length up to 24. We study all such quotients where the extra relator has length up to 36. Up to equivalence, th...

We investigate two arithmetic functions naturally occurring in the study of the Euler and Carmichael quotients. The functions are related to the frequency of vanishing of the Euler and Carmichael quotients. We obtain several results concerning the relations between these functions as well as their typical and extreme values.

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...