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# Tag Info

### $\pi$-adic Galois representations of attached to newforms at $p \nmid N$ are crystalline

Blasius and Rogawski's paper "Motives for Hilbert modular forms" (1993) proves a more general result for Hilbert modular forms over any totally-real field, which includes this as a special ...
Accepted

### Calculating the centralizer of a subgroup of $\mathrm{GL}(n, \mathbb{Z})$

There is an algorithm to do this (and also to test two matrices in ${\rm GL}(n,{\mathbb Z})$ for conjugacy) described in the paper: The conjugacy problem in ${\rm GL}(n,{\mathbb Z})$ Bettina Eick, ...

Accepted

### Geometric interpretation of Iwasawa algebras: $\mathbb{Z}_p[[T]]$ as a disk?

I give this answer just to make David's answer a little more general. Precisely, your $\Lambda$ should be thought as functions with norm less than $1$ in some Banach $\mathbb{Q}_p$-algebras. We fix a ...
Accepted

### Geometric interpretation of Iwasawa algebras: $\mathbb{Z}_p[[T]]$ as a disk?

The correct viewpoint is not "$\Lambda$ is like a disc", but "$\Lambda$ is like the functions on a disc". To see this, ask yourself: given an element $f \in \mathbb{Z}_p[[T]]$, ...
Accepted

### For a finite set A of positive reals, prove that the set A + A - A contains at least as many positive as negative elements

Here is a counterexample. We first need a "more sums than differences" construction: Lemma. For any $\varepsilon>0$ there exists a cyclic group ${\bf Z}/N{\bf Z}$ and a non-empty subset ...
Accepted

### Special configurations on a circle from a homological algebra problem

There is a simple characterization of interesting configurations: Lemma. A configuration $x_0=0< x_1 < x_2 < ... <x_r$ of Gorenstein dimension $g$ is interesting if and only if there exist ...

### Experiments with Voronoï summation

I think this is fine. Indeed, $S$ as a function of $B$ is of negligible size. This can also be checked as follows. Using Mellin transform and absolute convergence of the Dirichlet series of $\lambda$ ...

### Computing explicit isogenies between elliptic curves over different kinds of fields

For 1.1 and 1.2: Vélu's formulae require the kernel of the isogeny, or the polynomial whose roots are the $x$-coordinates of the nontrivial kernel points. If you don't know the isogeny in advance, but ...
Question 2 follows from Theorem 6.1 of arXiv:2101.02131. (In this reference, I consider $\prod_{i=1}^n(1+x^{F_{i+1}})$ rather than $\prod_{i=1}^n(1+x^{F_i})$, but the proof still works.) The result ...