Escuela de Matemática
Universidad de Costa Rica
San José 11501
Costa Rica
email: adrian.barquero_s@ucr.ac.cr
Office: 327 Edificio Anexo de Matemática (Ciudad de la Investigación)
B.S. in Mathematics, Universidad de Costa Rica (2011)
Ph.D. in Mathematics, Texas A&M University (2016)
Advisor: Riad Masri
My research focuses on number theory, with particular emphasis on problems related to automorphic forms, special values of L-functions, elliptic curves, Faltings heights of abelian varieties, algebraic number theory, the distribution of number fields, and the theory of complex multiplication.
The asymptotic distribution of Andrews' smallest parts function
With Josiah Banks, Riad Masri and Yan Sheng
Archiv der Mathematik (Basel) 105 (2015) no. 6, 539–555
PDF | Journal version
The Chowla-Selberg formula for abelian CM fields and Faltings heights
With Riad Masri
Compositio Mathematica 152 (2016) no. 3, 445–476
PDF | Journal version
Faltings heights of CM elliptic curves and special gamma values
With Lindsay Cadwallader, Olivia Cannon, Tyler Genao and Riad Masri
Research in Number Theory 3 (2017), Paper No. 13, 16 pp.
PDF | Journal version
On the Colmez conjecture for non-abelian CM fields
With Riad Masri
Research in the Mathematical Sciences 5 (2018), no. 1 Paper No. 10, 41 pp.
arXiv | Journal version
Theta series and number fields: theorems and experiments
With Guillermo Mantilla-Soler and Nathan C. Ryan
The Ramanujan Journal 56 (2021), no. 2, 613--630.
arXiv | Journal version
Stark units and special Gamma values
With Riad Masri and Wei-Lun Tsai
Research in Number Theory 7 (2021), no. 2, Paper No. 38, 40 pp.
Journal version
The distribution of G-Weyl CM fields and the Colmez conjecture
With Riad Masri and Frank Thorne
Research in the Mathematical Sciences 10 (2023), no. 2, Paper No. 25, 25 pp.
arXiv | Journal version
Efficient computation of the overpartition function and applications
With Gabriel Collado-Valverde, Nathan C. Ryan, Eduardo Salas-Jimenez, Nicolás Sirolli and Jean Carlos Villegas-Morales
Journal of Mathematical Analysis and Applications 528 (2023), no. 1, Paper No. 127472, 22 pp.
arXiv | Journal version
On the embedding of Galois groups into wreath products
With Jimmy Calvo-Monge
Communications in Algebra (2025) 53 (2), 730–760.
arXiv | Journal version
The density and distribution of CM elliptic curves over ℚ
With Jimmy Calvo-Monge
Journal of Mathematical Analysis and Applications 546 (2025), no. 1, Paper No. 129192, 23 pp.
arXiv | Journal version
On the efficient computation of Fourier coefficients of eta-quotients
With Juan Pablo De Rasis, Nicolás Sirolli and Jean Carlos Villegas-Morales
Submitted
arXiv
Explicit evaluations of Faltings heights of CM abelian varieties
With Riad Masri and Wei-Lun Tsai
In preparation
Counting elliptic curves over ℚ with bounded naive height
With Daniel Mora-Mora
Submitted
arXiv
I currently advise two master's students at the University of Costa Rica:
Daniel Mora-Mora
Master's student in Mathematics
Expected graduation: 2026
Greccio Porras-Herrera
Master's student in Mathematics
Expected graduation: 2026
Bucknell University's Distinguished Visiting Professor Program
Research visit and departmental colloquium
Colloquium talk: To be determined
Department of Mathematics, Bucknell University, Pennsylvania, United States
Scheduled for 2026
RNT 6: Rethinking Number Theory 6
Team co-leader with Nicolás Sirolli
Virtual workshop
June 16-27, 2025
Event website
CIMPA School on Serre's Open Image Theorem
Planned participation
Universidad de Valparaiso, Valparaiso, Chile
January 6-17, 2025
Event website
Number Theory in the Americas II
Team co-leader with Nicolás Sirolli
Casa Matemática Oaxaca, Oaxaca, Mexico
September 8-13, 2024
Event website
International Symposium on Mathematical Methods Applied to the Sciences (SIMMAC XXIV)
Talk: Efficient computation of the overpartition function and applications
Universidad de Costa Rica (Sede de Guanacaste), Liberia, Guanacaste, Costa Rica
February 20-23, 2024
Event website
Bayou Arithmetic Research Day 3
Plenary talk: "The distribution of CM fields and the Colmez conjecture"
Louisiana State University, Baton Rouge, Louisiana, USA
November 3, 2023
Event website