Related papers: Critical and asymmetric Fourier uniqueness pairs

We show that if a closed discrete subset $A \subseteq \mathbf{R}^d$ is denser than a certain critical threshold, then $A$ is a Fourier uniqueness set, while if $A$ is sparser, then uniqueness fails and one can prescribe arbitrary values for…

Motivated by recent works by Radchenko and Viazovska and by Ramos and Sousa, we find sufficient conditions for a pair of discrete subsets of the real line to be a uniqueness or a non-uniqueness pair for the Fourier transform. These…

The basis functions of the Fourier interpolation formula of Radchenko and Viazovska, constructed by means of weakly holomorphic modular forms for the Hecke theta group, are entire functions of order $2$ having interesting time-frequency…

We show an interrelation between the uniqueness aspect of the recent Fourier interpolation formula of Radchenko and Viazovska and the Heisenberg uniqueness study for the Klein-Gordon equation and the lattice-cross of critical density,…

We generalize the study of Heisenberg uniqueness pairs considered in earlier work with Alfonso Montes-Rodriguez. We also find the critical density in the case of one branch of the hyperbola. In the critical case there is non-uniqueness for…

We prove, under certain conditions on $(\alpha,\beta)$, that each Schwartz function $f$ such that $f(\pm n^{\alpha}) = \hat{f}(\pm n^{\beta}) = 0, \forall n \ge 0$ must vanish identically, complementing a series of recent results involving…

We classify the possible discrete (finite) symmetries of two--dimensional critical models described by unitary minimal conformally invariant theories. We find that all but six models have the group Z_2 as maximal symmetry. Among the six…

Odd-frequency Cooper pairs with chiral symmetry emerging at the edges of topological superconductors are a useful physical quantity for characterizing the topological properties of these materials. In this work, we show that the…

In this note, we prove a criteria for supersingularity when the variety has a large automorphism group and a perfect bilinear pairing. This criteria unifies and extends many known results on the supersingularity of curves and varieties and…

Synthetic nonconservative systems with parity-time (PT) symmetric gain-loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting…

In this paper, we extend Feigin-Frenkel duality at the critical level to complex rank by identifying two seemingly unrelated constructions in complex rank. On the affine side, we interpolate Molev's construction of higher Segal-Sugawara…

Let $K$ be a totally real number field of degree $n \geq 2$. The inverse different of $K$ gives rise to a lattice in $\mathbb{R}^n$. We prove that the space of Schwartz Fourier eigenfunctions on $\mathbb{R}^n$ which vanish on the…

In this paper, we show that any polynomial of zeta or $L$-functions with some conditions has infinitely many complex zeros off the critical line. This general result has abundant applications. By using the main result, we prove that the…

We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the Riemann zeta function and other $L$-functions. We establish…

We exhibit an asymmetry phenomenon for uniqueness sets in $\ell^q$. Specifically, we construct sets that do not support measures with $\ell^q$-summable Fourier coefficients, yet simultaneously support measures whose positive frequencies…

There is extensive numerical support for the prime-pair conjecture (PPC) of Hardy and Littlewood (1923) on the asymptotic behavior of pi_{2r}(x), the number of prime pairs (p,p+2r) with p not exceeding x. However, it is still not known…

We consider the class of Rudin-Shapiro-like polynomials, whose $L^4$ norms on the complex unit circle were studied by Borwein and Mossinghoff. The polynomial $f(z)=f_0+f_1 z + \cdots + f_d z^d$ is identified with the sequence…

Here we study problems related to the proportions of zeros, especially simple and distinct zeros on the critical line, of Dedekind zeta functions. We obtain new bounds on a counting function that measures the discrepancy of the zeta…

We provide weak-type bounds for a family of bilinear fractional integrals that arise in the study of Euler-Riesz systems. These bounds are uniform in the natural parameter that describes the family and are sharp, in the sense that they do…

These notes are devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension two and higher interpolate between Poincar\'e, logarithmic Sobolev and critical Sobolev (Onofri in dimension…