All Questions
9 questions with no upvoted or accepted answers
9
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0
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2k
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Exactly Counting the Number of Lattice Points in an $n$-Dimensional Sphere
Let $S_n(R)$ denote the number of lattice points in an $n$-dimensional "sphere" with radius $R$. For clarification, I am interested in lattice points found both strictly inside the sphere, and on its ...
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4
votes
0
answers
81
views
Classification of nilpotent orbits over local fields (for type ABCD via partitions )
Let $\mathfrak g$ be a simple Lie algebra over a char $0$ local field $F$ (e.g. $F=\mathbb R$ or $F=\mathbb Q_p$) with its adjoint group $G$. Let $\mathcal N \subseteq \mathfrak g$ be its nilpotent ...
- 6,622
4
votes
0
answers
384
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Parity in degrees of determinantal varieties
Let $M_{m,n}(\Bbb{C})$ be the space of $m\times n$ matrices with entries in $\Bbb{C}$, and let $U_{k,m.n}(\Bbb{C})\subset M_{m,n}(\Bbb{C})$ be the variety of matrices of rank $\leq k\leq\min(m,n)$. ...
- 43.2k
4
votes
0
answers
371
views
How is $ \sum_{x \in X(\mathbb{F}_q)} \dots $ a generalization of cardinality?
This quarter Maxim Kontsevich is offering a course on exponential integral. There is not much in the way of notes, but is one page with mysterious comments.
Let $X$ be an algebraic variety over $\...
- 22.8k
3
votes
0
answers
243
views
Interlacing sequences by polynomials?
Given $t=2^\ell$ where $\ell\in\mathbb N_{>0}$ and $M\in\mathbb Z$ and two sets of integers $\{a_1,\dots,a_t\}$ and $\{b_1,\dots,b_t\}$ with $0<a_1\leq \dots\leq a_t<M$ and $0<b_1\leq \...
- 13.9k
3
votes
0
answers
148
views
Maximum number of integral roots in degree $d$ polynomial?
Given $f(x_1,\dots,x_n)\in\mathbb Z[x_1,\dots,x_n]$ such that
Each coefficient is bound in absolute value by $B$
Degree of each variable in any monomial is bound by $d$
Total degree is $d'$
$f(x_1,\...
- 13.9k
1
vote
0
answers
162
views
Difficulty understanding a step in the proof of multiset version of Cauchy-Davenport Theorem
In a paper "G. Kós, L. Rónyai, Alon’s Nullstellensatz for multisets, Combinatorica, 32(5) (2012) 589-605", the authors prove a multiset version of the Cauchy-Davenport Theorem (please see ...
- 167
0
votes
0
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54
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Functional equations with coupled arguments and additive sructure
Let $G$ be a locally compact abelian group and let $f: G \to \mathbb{R}^+$ be a continuous function satisfying the functional equation
$$f(x + \phi(y)) + f(y + \phi(x)) = 1 + f(x+y)$$
for all $x, y \...
0
votes
0
answers
67
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Neccessary and sufficient condition for trivial rational solution of rational homogeneous cubic polynomials
If we consider a cubic homogeneous polynomial in $ 5 $ variables , $ ax_{1}^{3} + bx_{2}^{3} + cx_{3}^{3} + dx_{4}^{3} + ex_{5}^{3} + \sum_{i < j<k =1}^{5} f_{ijk} x_{i}x_{j}x_{k} $ where a,b,c,...
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