9 papers
The Erdős similarity conjecture and Rajchman measures
A. Iosevich, N. Kulkarni, N. Mora Cuéllar +2
Let support a probability measure whose Fourier--Stieltjes transform tends to zero at infinity. We prove that, for every , there is a cl…
The Erdős Similarity Conjecture for Two-Fold Sumsets with a Geometric Summand
N. Mora Cuellar, A. Iosevich, N. Kulkarni +2
We settle a major case in the two-set regime of the Erdős similarity conjecture: the sum of a geometric sequence and an arbitrary infinite set is never measure universal. Here a se…
Fourier Ratios of Graph Kernels: Energy Bounds, Optimal Labelings, and Recovery
Vishal Gupta, Alex Iosevich
We study labeling-sensitive Fourier complexity for finite graph kernels. After identifying the vertices of a graph with the cyclic group , its adjacency matrix becomes…
Elliptic curves, Fourier ratio, and sampling complexity
W. Burstein, A. Iosevich, A. Sant
We study the normalized Frobenius trace associated with the Legendre family of elliptic curves over from the point of view of Fourier complexity. If \[ f(t)=\frac{a_p…
Metric entropy of Fourier ratio classes on
Alex Iosevich, Vahagn Hovhannisyan, Zahra Keyshams +1
We study metric entropy and uniform sampling for classes of signals on with prescribed Fourier ratio. The Fourier ratio measures how spread out the Fourier transfor…
Large values in time series and additive combinatorics
Alex Iosevich, Vishal Gupta
It is well-known in industrial data science that large values of real-life time series tend to be structured and often follow concrete and visible patterns. In this paper, we use i…
Arithmetic functions and learning theory
W. Burstein, A. Iosevich, A. Sant
We establish a connection between analytic number theory and computational learning theory by showing that the Möbius function belongs to a class of functions that is statistically…
Falconer lattice sets and the Erdos similarity problem
A. Iosevich, A. Yavicoli
We show that a family of extremely thin sets satisfy the Erdős similarity conjecture. These examples lie outside the range covered by recent work of Shmerkin and Yavicoli \cite{Shm…
Buffon Needle Problem Over Convex Sets
M. Dannenberg, W. Hagerstrom, G. Hart +4
We solve a variant of the classical Buffon Needle problem. More specifically, we inspect the probability that a randomly oriented needle of length originating in a bounded conv…