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Consider a function whose Fourier transform is supported on a half-ray: $$ A(t)=\int_0^\infty \omega(E) e^{-iEt}d E, $$ where I can suppose $\omega(E)\geq 0$ and any suitable regularity conditions on $...

Assume $G(q,z)$ is a Jacobi form of a certain index k. It is known that $G$ can be expanded in a Taylor series with coefficients in the ring of quasi-modular forms (generators $E_2, E_4$ and $E_6$). $\...

I've seen many trigonometric identities but here is one that I encountered for which I did not find a reference. In case you wonder where this came from, I was investigating certain $q$-series in ...

Let $z=e^{2\pi i\theta}$ for a fixed real number $\theta$. It's known that if $\theta\not\in\mathbb{Q}$ (is irrational) then the set $S(\theta)=\{z^n: n\in\mathbb{N}\}$ is dense on the unit circle $\...

Let $u(t) = \Sigma_{k=1}^n c_k e^{i \lambda_k t} (c_k \in \mathbb C, \lambda_k \in \mathbb R) $ be an exponential polynomial of order $n$ with purely imaginary exponents. We can assume that the ...

The original post The following argument appears in a paper of Nazarov (Lemma 1.2) "Local estimates for exponential polynomials and their applications to inequalities of the uncertainty principle ...