We count algebraic points of bounded height and degree on the graphs certain functions analytic unit disk, obtaining a bound which is polynomial in logarithm multiplicative height. combine this work with $p$-adic methods to obtain, for each positive $\varepsilon$, an upper form $cD^{3n/4 + \varepsilon n}$ number irreducible factors $P^{\circ n}(X)-P^{\circ n}(\alpha)$ over $K$, where $K$ field,...

We Propose A Novel Automaton Model which uses Arithmetic Operations as the Evolving Rules, each cell has the states of the Natural Numbers k = (N), a radius of r = 1 2 and operates on an arbitrary input size. The Automaton reads an Arithmetic Expression as an input and outputs another Arithmetic Expression. In Addition, we simulate a variety of One Dimensional Cellular Automata Structures with ...

LetM be a complete Riemannian manifold with finite volume which we initially assume to be compact. Then since M is compact, L(M) is spanned by the eigenfunctions of the Laplacian ∆ on M . Many interesting questions can be asked about these eigenfunctions and their properties, and of these we focus on one, quantum ergodicity, which to the best of my knowledge was first considered by A. I. Šnirel...