Related papers: Modulus triples
We study the structures of arbitrary split Leibniz triple systems. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of $T$ being of maximal length, the simplicity of the…
We study the Modular Isomorphism Problem applying a combination of existing and new techniques. We make use of the small group algebra to give a positive answer for two classes of groups of nilpotency class 3. We also introduce a new…
We study modular forms of some congruence subgroups. In this paper, we treat the cases level is 2-power, 3-power or 5. Structures of graded rings and many identities of infinite sum or infinite product are given. Theory of rational (1/3,…
We prove the modularity of a positive proportion of abelian surfaces over $\mathbf{Q}$. More precisely, we prove the modularity of abelian surfaces which are ordinary at $3$ and are $3$-distinguished, subject to some assumptions on the…
The Pythagorean triples have the structure of a ternary rooted tree; the tree is based on the Cayley graph of a free subgroup of the modular group
Let $M$ be a finitely generated module over a ring $\Lambda$. With certain mild assumptions on $\Lambda$, it is proven that $M$ is a reflexive $\Lambda$-module, once $M \cong M^{**}$ as a $\Lambda$-module.
We prove some cycle relations on moduli of K3 surfaces
In this article, we give an unconditional definition of the motivic analogue of the intersection complex, establish its basic properties, and prove its existence in certain cases.
Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic:…
We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.
We will invest quite some computer power to find double octic threefolds that are connected to weight four modular forms.
We develop a "motivic integration" version of the Poisson summation formula for function fields, with values in the Grothendieck ring of definable exponential sums. We also study division algebras over the function field, and obtain…
In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.
We extend the scope of a former paper to vector bundle problems involving more than one vector bundle. As the main application, we obtain the solution of the well-known moduli problems of vector bundles associated with general quivers.
We compute the motivic nearby cycles of functions obtained by composition of two functions with distinct sets of variables with a two variable function
In this work we extend the concept of the Lipschitz saturation of an ideal defined in [5] to the context of modules in some different ways, and we prove they are generically equivalent.
We review some results and techniques from our papers devoted to the computation of motivic classes of stacks of parabolic Higgs budles and bundles with connections on a curve. In the last section we present some directions for future work,…
In this paper, we construct some maps related to the motivic Galois action on depth-graded motivic multiple zeta values. And from these maps we give some short exact sequences about depth-graded motivic multiple zeta values in depth two and…
We propose a simple model of recognition, short-term memory, long-term memory and learning.
This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors…