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

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4 papers · 1 filter

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…

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

Heath-Brown identities for fractional powers of $ζ$