I study analytic number theory, particularly on the arithmetic and analytic properties of modular forms and its applications. I also study number theory according to Ramanujan, including but not limited to elementary q-series techniques and dissection formulas.

For correspondence, you may reach me at Google Scholar, ResearchGate, and ORCID, or contact me through my email above.

Mentoring Activities

Current undergraduate advisees (for Second Semester AY 2024-25)

1. Art James Symon Siat (BS Math)

Past undergraduate co-advisees

1. Charles Justin Shi (BS Math, First Semester AY 2024-25, Adviser: Dr. VM Aricheta)

Second Semester AY 2024-2025

• Math 117 THW: TTh 13:00-14:30, MBAN 307
• Math 197 THX: TTh 14:30-16:00, MBAN 307
• Math 200

Consultation Hours: TTh 16:00-18:00, WF 13:00-16:00

First Semester AY 2024-2025

• Math 21 TWHFQ6 (as faculty-in-charge): TTh 07:15-08:15, MB 307
• Math 21 TWHFR7 (as faculty-in-charge): TTh 08:45-09:45, MB 307
• Math 21 TWHFW7: TTh 13:15-14:15, MB 307
• Math 200 (with Dr. VM Aricheta)
• Math 217 THX: TTh 14:30-16:00, MB 116

Courses Previously Taught

• Math 14
• Math 17
• Math 21, 22, 23
• Math 53, 54
• Math 117 (briefly)

Refereed Papers

1. Guadalupe, R, Asymptotic formulas for some $3$-color partitions, to appear in  J. Anal.
2. Guadalupe, R, A remark on generalized cubic partitions modulo $5$, to appear in Bull. Aust. Math. Soc.
3. Guadalupe, R, Modularity of certain products of the cubic continued fraction, J. Korean Math. Soc. (2025)
4. Guadalupe, R, A conjecture of Pore and Fathima on congruences modulo $20$ for Andrews’ partition function, Bol. Soc. Mat. Mex. (3) 31 (2025), paper no. 45, 6 pp.
5. Guadalupe, R, A note on congruences for generalized cubic partitions modulo primes, Integers 25 (2025), #A20.
6. Guadalupe, R, Aricheta, VM, Analogue of Ramanujan’s function $k(\tau )$ for the continued fraction $X(\tau )$ of order six, Ann. Univ. Ferrara Sez. VII Sci. Mat. 71 (2025), paper no. 6, 18 pp.
7. Guadalupe, R, A note on the exact formulas for certain $2$-color partitions, C. R. Math. Acad. Sci. Paris 362 (2024), 1485-1490.
8. Guadalupe, R, Modularity of a certain continued fraction of Ramanujan, Ramanujan J. 63 (2024), 947-967.
9. Guadalupe, R, Celeste, R, Modularity of generalized Weber functions $v_{l,k,N/l}$, Matimyas Mat. 45 (2022), 1-12. 

Preprints

1. Remarks on a certain restricted partition function of Lin
2. New Gosper’s Lambert series identities of levels $12$ and $16$
3. Gosper’s Lambert series identities of level $14$
4. A remark on modular equations involving Rogers-Ramanujan continued fraction via 5-dissections
5. Modularity of certain products of the Rogers-Ramanujan continued fraction
6. Ramanujan’s continued fractions of order $10$ as modular functions (with VM Aricheta)

For preprints before 2024, please visit this arXiV link.