# Tagged Questions

The tag has no usage guidance.

667 views

374 views

### A condition for a sequence defined by a recurrence relationship to all be integers

I am interested in a specific sequence $\{a_n \}$ defined by a simple recurrence relationship: $$a_n = \frac {a_{n-1} ^2 +c} {b}$$ where $b,c\in \mathbb{Z}$. I want to find all $b,c$ such that there ...
225 views

### Growth of the size of iterated polynomials

I have been working independently on a project but now I am stuck and need to seek an expert's wisdom for a part of it. I am basically looking for theorems related to growth of the size of polynomials....
165 views

### A probability application question

Suppose there are two possible states $H$ and $L$, with prior probability $p$ and $1-p$ respectively. There are infinite rounds with a discount factor $d$. In round 1, you could choose a value $t_1$...
110 views

### Equidistribution of double coset

Let $G=PGL_n(\mathbb{R})$, $K=PO_n(\mathbb{R})$ and $X=G/K$. Also suppose $\Gamma=SL_n(\mathbb{Z})$ acts on the left of $X$. We define a typical Hecke operator on $L^2(\Gamma\backslash X)$ by the ...
139 views

### Indeterminancy locus of rational maps

Let $K=\bar{\mathbb{Q}}(\mathbb{P}^2_\bar{\mathbb{Q}})$, the function field of $\mathbb{P}^2_\bar{\mathbb{Q}}$. Let $C/K$ be a smooth projective curve over $K$ in $\mathbb{P}^2_K$ and let $f$ be a ...
275 views

### Reducibility of polynomials maps

Motivated by this question. Let $f \in \mathbb{Q}[x]$ or$f \in \mathbb{Z}[x]$ . Consider the sequence $f(x),f(f(x)), \ldots f^n(x)$. If some $f^k(x)$ is reducible, the rest iterates will be ...
550 views

### Generating primes via composition of polynomials

It is well known that no nonconstant polynomial $f\in \mathbb{Z}[x]$ can assume only prime values at integer arguments. Indeed, if $a\in \mathbb{Z}$ is so large that $|f(a)|>1$, and if $p$ is a ...
1k views

### Arithmetic dynamics and dynamics on moduli spaces

The following question is more of a request for pointers to suitable literature on introductory material for arithmetic dynamics and dynamics on moduli spaces. In my dissertation, I have been ...
Hi, Is there any way of moving from one cat map transformation to the other without resetting parameters? For example, suppose you have two matrices '$A$'and '$B$' each permuted with different cat ...