About Me

I'm an assistant professor at the Universidade Federal do Ceará. Prior to that I was a visiting scholar at the Max Planck Institute for Mathematics hel a visiting professorship at the Universidae Federal do Ceará and a post-doctoral position at the École Polytechnique Fédérale de Lausanne, mentored by Philippe Michel. I did my Phd at the Université Paris-Sud. My Phd advisor was Étienne Fouvry.

My reasearch interests lie in Analytic Number Theory, Automorphic forms, L-functions and trace formulae.

Publications

Preprints

Strong Hybrid Subconvexity for Twisted Selfdual $\mathrm{GL}_3$ $L$-Functions Soumendra Ganguly, Peter Humphries, Yongxiao Lin, Ramon Nunes arXiv (2024).
arXiv DOI
We prove strong hybrid subconvex bounds simultaneously in the $q$ and $t$ aspects for $L$-functions of selfdual $ \mathrm{GL}_3$ cusp forms twisted by primitive Dirichlet characters. We additionally prove analogous hybrid subconvex bounds for central values of certain $ \mathrm{GL}_3 \times \mathrm{GL}_2$ Rankin-Selberg $L$-functions. The subconvex bounds that we obtain are strong in the sense that, modulo current knowledge on estimates for the second moment of $ \mathrm{GL}_3$ $L$-functions, they are the natural limit of the first moment method pioneered by Li and by Blomer. The method of proof relies on an explicit $ \mathrm{GL}_3 \times \mathrm{GL}_2 \leftrightsquigarrow \mathrm{GL}_4 \times \mathrm{GL}_1$ spectral reciprocity formula, which relates a $\mathrm{GL}_2$ moment of $ \mathrm{GL}_3 \times \mathrm{GL}_2$ Rankin-Selberg $L$-functions to a $ \mathrm{GL}_1$ moment of $ \mathrm{GL}_4 \times \mathrm{GL}_1$ Rankin-Selberg $L$-functions. A key additional input is a Lindelöf-on-average upper bound for the second moment of Dirichlet $L$-functions restricted to a coset, which is of independent interest.
Moments of $L$-Functions via the Relative Trace Formula Subhajit Jana, Ramon Nunes arXiv (2023).
arXiv DOI
We prove an asymptotic formula for the second moment of the $\mathrm{GL}(n)\times\mathrm{GL}(n+1)$ Rankin--Selberg central $L$-values $L(1/2,\Pi\otimes\pi)$, where $\pi$ is a fixed cuspidal representation of $\mathrm{GL}(n)$ that is tempered and unramified at every place, while $\Pi$ varies over a family of automorphic representations of $\mathrm{PGL}(n+1)$ ordered by (archimedean or non-archimedean) conductor. As another application of our method, we prove the existence of infinitely many cuspidal representations $\Pi$ of $\mathrm{PGL}(n+1)$ such that $L(1/2,\Pi\otimes\pi_1)$ and $L(1/2,\Pi\otimes\pi_2)$ do not vanish simultaneously where $\pi_1$ and $\pi_2$ are cuspidal representations of $\mathrm{GL}(n)$ that are unramified and tempered at every place and have trivial central characters.
Spectral Reciprocity for $\mathrm{GL}(n)$ and Simultaneous Non-Vanishing of Central $L$-Values Subhajit Jana, Ramon Nunes Accepted, American Journal of Mathematics (2021).
arXiv DOI
We prove a reciprocity formula for the average of the product of Rankin--Selberg $L$-functions $L(1/2,\Pi\times\widetilde\sigma)L(1/2,\sigma\times\widetilde\pi)$ as $\sigma$ varies over automorphic representations of $\mathrm{PGL}(n)$ over a number field $F$, where $\Pi$ and $\pi$ are cuspidal automorphic representations of $\mathrm{PGL}(n+1)$ and $\mathrm{PGL}(n-1)$ over $F$, respectively. If $F$ is totally real, and $\Pi$ and $\pi$ are tempered everywhere, we deduce simultaneous non-vanishing of these $L$-values for certain sequences of $\sigma$ with conductor tending to infinity in the level aspect and bearing certain local conditions.

Published Articles

Spectral Reciprocity via Integral Representations Ramon M. Nunes Algebra & Number Theory (2023).
arXiv DOI
We prove a spectral reciprocity formula for automorphic forms on $\mathrm{GL}(2)$ over a number field that is reminiscent of one found by Blomer and Khan. Our approach uses period representations of L-functions and the language of automorphic representations.
Strong Subconvexity for Self-Dual $\mathrm{GL}(3)$ $L$-Functions Yongxiao Lin, Ramon Nunes, Zhi Qi International Mathematics Research Notices (2022).
arXiv DOI
In this paper, we prove strong subconvexity bounds for self-dual $\textrm{GL}(3)$ $L$-functions in the $t$-aspect and for $\textrm{GL(3)}\times\textrm{GL}(2)$ $L$-functions in the $\textrm{GL}(2)$-spectral aspect. The bounds are strong in the sense that they are the natural limit of the moment method pioneered by Xiaoqing Li, modulo current knowledge on estimate for the second moment of $\textrm{GL}(3)$ $L$-functions on the critical line.
Moments of the Distribution of $k$-Free Numbers in Short Intervals and Arithmetic Progressions Ramon M. Nunes Bulletin of the London Mathematical Society (2022).
DOI
We show estimates for the distribution of $k$-free numbers in short intervals and arithmetic progressions that, in certain ranges, agree with a conjecture by Montgomery.
The Twelfth Moment of Dirichlet L-functions with Smooth Moduli Ramon M Nunes International Mathematics Research Notices (2021).
DOI
We prove an analogue of Heath-Brown's bound on the 12th moment of the Riemann zeta function for Dirichlet $L$-functions with smooth moduli.
On Bourgain's bound for short exponential sums and squarefree numbers Ramon M. Nunes Acta Arithmetica (2016).
DOI
We use Bourgain's recent bound for short exponential sums to prove certain independence results related to the distribution of squarefree numbers in arithmetic progressions.
Squarefree Numbers in Arithmetic Progressions Ramon M. Nunes Journal of Number Theory (2015).
DOI
We give asymptotics for correlation sums linked with the distribution of squarefree numbers in arithmetic progressions over a fixed modulus. As a particular case we improve previous results concerning the variance.