# Tagged Questions

56 views

### Are major arcs always around a fraction with small denominator? [on hold]

In the usual circle method we might have a trigonometric polynomial $F(\theta)=\sum_{n}a_n e(n\theta)$ and we need to estimate the integral $\int_0^1 F(\theta)d\theta$ by breaking the domain into ...
350 views

### Correlation of Fourier transforms of characteristic functions

Let $A$ and $B$ ($A\subset B$) be subsets of a finite abelian group $G$. (For the sake of argument, you can take $G$ to be $\mathbb{Z}/p\mathbb{Z}$ for large $p$, say.) Write $1_S$ for the ...
629 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 ...
373 views

### Fourier analysis, orthogonality, and Plancherel for finite abelian groups

I am reading an outstanding paper by Bateman and Katz, improving the best known bounds on the cap set problem (Roth's theorem over $\mathbb{F}_3^N$). The paper contains some technical lemmas for ...
827 views

### Choice of normalization of the finite Fourier transform

Let $f : \mathbb{Z}/N\mathbb{Z} \rightarrow \mathbb{C}$ be a function. Is its Fourier transform typically defined by \widehat{f}(\xi) = \sum_{x \in \mathbb{Z}/N \mathbb{Z}} f(x) e^{- 2 \pi i x \xi ...
Elon Lindenstrauss explains in his talk at the MSRI in Fall 2008 (the relevant comment is at minute 41 of the video) that the set of large Fourier coefficients of a probability measure $\mu$ on the ...