Nicolas Robles

activity

20132026

most citedA variational quantum algorithm for the Feynman-Kac formula

34 citations · 82 across the 16 of their papers we have counts for

collaborators

23 papers

math.NT2026

A folklore conjecture on multiplicative exponential sums

Nicolas Robles

We prove a folklore conjecture on exponential sums with multiplicative coefficients: if $f$ is multiplicative with $∣ f (n) ∣ \leq 1$ , $(a, q) = 1$ , $∣ α - a / q ∣ \leq q^{- 2}$ and $q\le N/(\log N)…

math.NT2026

Effective estimates for exponential sums with multiplicative coefficients

Nicolas Robles

Let $f$ be multiplicative, with $∣ f (p) ∣ \leq A$ at primes and $\sum_{n \leq x} ∣ f (n) ∣^{2} \leq A^{2} x$ for every $x \geq 1$ . If $∣ α - a / q ∣ \leq q^{- 2}$ , $(a, q) = 1$ , and $3 \leq R \leq q \leq N / R$ , we prove…

math.NT2026

On the exponential sum over squarefree integers

Nicolas Robles, Alexandru Zaharescu, Dirk Zeindler

Let $μ$ be the Möbius function and $e (t) = e^{2 π i t}$ . We prove that if $N \geq 2$ , $α \in R$ , $(a, q) = 1$ , and $∣ α - a / q ∣ \leq q^{- 2}$ , then \[\bigg|\sum_{n\le N}μ^2(n)e(αn)\bigg|\ll\l…

math.NT2026

Heath-Brown identities for fractional powers of $ζ$

Nicolas Robles

We construct finite Heath-Brown-type identities for the fractional powers $ζ (s)^{\pm a / b}$ of the Riemann zeta-function, for every reduced fraction $a / b$ with $0 < a / b < 1$ , from N…

math.NT2025

An Analogue of the Dedekind Eta Function for Hecke Groups $H (D)$

Debmalya Basak, Dorian Goldfeld, Winston Heap +2

Let $D \equiv 1 mod 4$ be a fundamental discriminant of a real quadratic field. We construct an analogue of the classical Dedekind eta function for the Hecke group $H (D)$ .…

math.NT2024

Exponential sums twisted by general arithmetic functions

Anji Dong, Nicolas Robles, Alexandru Zaharescu +1

We examine exponential sums of the form $\sum_{n \leq X} w (n) e^{2 π i α n^{k}}$ , for $k = 1, 2$ , where $α$ satisfies a generalized Diophantine approximation and where $w$ are different arit…

A folklore conjecture on multiplicative exponential sums

Effective estimates for exponential sums with multiplicative coefficients

On the exponential sum over squarefree integers

Heath-Brown identities for fractional powers of ζ

An Analogue of the Dedekind Eta Function for Hecke Groups H(D​)

Exponential sums twisted by general arithmetic functions

Heath-Brown identities for fractional powers of $ζ$

An Analogue of the Dedekind Eta Function for Hecke Groups $H (D)$