Nicolas Robles

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math.NT2026

Bilinear forms with Kloosterman fractions and applications

Anji Dong, Nicolas Robles, Dirk Zeindler

We establish improved bounds for bilinear forms with Kloosterman fractions of the form $\sum\sum_{m, n} α_{m} β_{n} e (a m / (bn))$ with $M < m \leq 2 M$ , $N < n \leq 2 N$ and $(m,n)=…

math.NT2025

A central limit theorem for partitions involving generalised divisor functions

Madhuparna Das, Nicolas Robles

We let $p_{f} (n, k)$ count the $f$ -restricted coloured partitions of $n$ with $k$ parts, for a positive integer valued function $f$ , given by the bivariate generating series \[ Q_f(z,…

math.NT2025

Exponential sums weighted by additive functions

Ayla Gafni, Nicolas Robles

We introduce a general class $F_{0}$ of additive functions $f$ such that $f (p) = 1$ and prove a tight bound for exponential sums of the form $\sum_{n \leq x} f (n) e (α n)$ where $f \in…