All Questions
Tagged with exponential-sums additive-combinatorics
7 questions
14
votes
1
answer
2k
views
On the $L^1$-norm of certain exponential sums
I am stuck with an elementary-looking problem, which does not belong to my usual field of research so I eventually decided to ask it on MO.
Let $S$ be a finite set of integers. For $P$ a subset of $S$,...
- 26k
10
votes
1
answer
706
views
Why are exponential sums so bad at solving this very easy problem?
Exponential sums are a powerful tool in additive combinatorics and number theory. In my understanding, when it comes to estimate the cardinality of a certain set, exponential sums are (essentially) ...
- 103
5
votes
0
answers
370
views
Lower bound for some sums of roots of unity
Let $n$ be a positive integer (assume $n$ is prime for simplicity), and let $x_k = \pm1$, for $k = 0,1,2,..., n-1$. Let $\rho$ be an $n-$th primitive root of unity, I am interested in a lower bound ...
- 1,101
3
votes
0
answers
467
views
Solving a doubly exponential generating function
I am analyzing the average time complexity of some algorithm on some probabilistic model, and I've come to a doubly exponential sequence for which I cannot find corresponding generating function. I ...
- 396
2
votes
1
answer
97
views
Elaboration of a certain section of a paper by Thanigasalam
In section 11 of this paper by Thanigasalam, it says "... we get $G(10)\le 105$, and this implies that $H(10) \le 107$". However, it is very unclear how this follows. Why is it the case that $G(10)\le ...
- 1,890
0
votes
1
answer
85
views
What is the maximal number of solutions of $\sum_{i = 1}^n 1/a_i^x - \sum_{i = 1}^m 1/b_i^x = 0$?
What is the maximal number of solutions of the following equation?
$\sum_{i = 1}^n 1/a_i^x - \sum_{i = 1}^m 1/b_i^x = 0$
where $x$ is the unknown and $n, m$, $a_i$'s, $b_i$'s are constant.
It ...
- 377
0
votes
0
answers
70
views
$\ell^2 \rightarrow L^p ([0,1]^d) $ estimates for trigonometric polynomials
My question concerns $L^p ([0,1]^d)$ estimates for trigonometric polynomials, where both the coefficients and frequencies are coming from general (i.e. not necessarily geometrically special/structured)...
