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Giulia Cesana

Publications and source records attributed to Giulia Cesana.

4 recordsLinked to original sources
arXiv2023

Sums of proper divisors with missing digits

Let $s(n)$ denote the sum of proper divisors of an integer $n$. In 1992, Erdős, Granville, Pomerance, and Spiro (EGPS) conjectured that if $\mathcal{A}$ is a set of integers with asymptotic density zero then $s^{-1}(\mathcal{A})$ also has asymptotic density zero. In this paper we show that the EGPS conjecture holds when $\mathcal{A}$ is taken to be a set of integers with missing digits. In particular, we give a sharp upper bound for the size of this preimage set. We also provide an overview of progress towards the EGPS conjecture and survey recent work on sets of integers with missing digits.

math.NT↗
arXiv2023

Fourier Coefficients of Weight Zero Mixed False Modular Forms

In this paper we employ the Circle Method to give exact formulae for Fourier coefficients of an infinite family of weight zero mixed false modular forms using and extending the techniques of Bringmann and Nazaroglu as well as Rademacher. To do so we additionally provide a bound on a Kloosterman sum of modulus $k$.

math.NT↗
arXiv2021

Asymptotic equidistribution for partition statistics and topological invariants

We provide a general framework for proving asymptotic equidistribution, convexity, and log concavity of coefficients of generating functions on arithmetic progressions. Our central tool is a variant of Wright's Circle Method proved by two of the authors with Bringmann and Ono, following work of Ngo and Rhoades. We offer a selection of different examples of such results, proving asymptotic equidistribution results for several partition statistics, modular sums of Betti numbers of two- and three-flag Hilbert schemes, and the number of cells of dimension a (mod b) of a certain scheme central in work of Göttsche.

math.NT↗