Ramon Nunes

Assistant Professor of Mathematics

Universidade Federal do Ceará

Biography

My reasearch interests lie in Number theory. More specifically, in Analytic Number Theory. I am also interested in Automorphic forms, specially in its applications to Number Theory.

Interests

• Analytic Number Theory
• Automorphic forms
• $L$-functions

Education

• PhD in Mathematics, 2015

  Université Paris-Sud

• Masters degree in Mathematics, 2012

  Université Paris-Sud

• BSc in Mathematics, 2011

  Universidade Federal do Ceará

Experience

 

 

 

 

 

Assistant Professor

Universidade Federal do Ceará

October 2021 – Present Fortaleza

Responsibilities include:

• Participating in boring meetings
• Grading exams
• Attending badly-designed courses on improving teaching habilities

 

 

 

 

 

Visiting Scholar

Max-Planck Institut für Mathematik

October 2021 – October 2022 Bonn

 

 

 

 

 

Visiting Professor

Universidade Federal do Ceará

April 2019 – March 2021 Fortaleza

Research and minimal teaching

Recent Posts

Results concerning automorphic forms and L-functions of higher rank

Motivating goal: Subconvexity for twists \(F\) is a number field. \(\pi:\mathrm{GL}_n\), \(\chi:\mathrm{GL}_1\) \[\begin{align} \label{subconvex-twists} L(\pi\times\chi,&1/2)\ll_\pi C(\chi)^{n/4-\delta}\tag{$\star$} \\ &\Bigg\updownarrow \substack{\text{(Lapid-Mao) $n$ is even, $\pi$ comes from $\mathrm{SO}(n+1)$},\\ \text{$\chi$ quadratic, $C_\mathrm{fin}(\chi)\approx\square$-free}}\notag\\ \text{Fourier} & \text{ coefficients on $Mp_n$}\notag \end{align}\]

Sep 14, 2023 2 min read

Análise complexa - aula 6

Fórmula de Cauchy Teorema 1. Seja \(f: \Omega \rightarrow \mathbb{C}\) uma função holomorfa e seja \(D = D_{\delta}(z_0)\) tal que \(\overline{D} \subseteq \Omega\). Se \(C\) denota o bordo de D no sentindo positivo.

Sep 12, 2023 4 min read

Análise complexa - aula 5

Na aula passada, vimos que se \(f\) é holomorfa em um dimínio contendo um triângulo T em seu interior, então \[\int_{T}f(z)dz = 0.\] Agora, vamos usar esse resultado para provar o teorema seguinte.

Sep 12, 2023 4 min read

Análise complexa - aula 4

Curvas (continuação) Definição 1. A equivalência de curvas, definida na aula passada é, de fato, uma relação de equivalência e uma curva é uma classe de equivalência de curvas parametrizadas.

Aug 29, 2023 6 min read

Análise complexa - aula 3

Aula de hoje: série de potências. Exemplo: \[e^x =1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+...\] converge para todo \(x\) real e define uma função(infinitamente) diferenciável. Hoje vamos ver, dentre outras coisas que \(e^z = 1+z+\frac{z^2}{2!}+ \frac{z^3}{3!}+\cdots\) converge para todo \(z\in \mathbb{C}\) e define uma função holomorfa.

Aug 29, 2023 5 min read

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Projects

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All Notas Other

Notas do curso de Análise complexa

Semestre 2023.3 - TeX por Pedro Igor

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Recent Publications

Yongxiao Lin, Ramon Nunes, Zhi Qi (2022). Strong Subconvexity for Self-Dual GL(3) L-Functions. International Mathematics Research Notices.

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Ramon M. Nunes (2022). Moments of the Distribution of $k$-Free Numbers in Short Intervals and Arithmetic Progressions. Bulletin of the London Mathematical Society.

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Ramon M. Nunes (2021). Spectral Reciprocity via Integral Representations. arXiv.

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Subhajit Jana, Ramon Nunes (2021). Spectral Reciprocity for GL$(n)$ and Simultaneous Non-Vanishing of Central $L$-Values. arXiv.

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Ramon M Nunes (2021). The Twelfth Moment of Dirichlet L-functions with Smooth Moduli. International Mathematics Research Notices.

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Recent & Upcoming Events

Automorphic Forms and L-functions of higher rank

Sep 11, 2023 9:00 AM — Sep 15, 2023 4:00 PM Queen Mary London University

Thematic Session - Analytic Number Theory

Jul 27, 2023 2:15 PM — Jul 28, 2023 6:30 PM IMPA

Popular Topics

11A07 (secondary) 11F55 11F72 11N37 (primary) Arithmetic progressions Exponential sums Mathematics - Number Theory notas-de-aula Squarefree integers