Guadalupe, Russelle
Analytic number theory (modular forms)
- Coding and Number Theory (member)
- Groups, Geometry, and Representations (affiliate)
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Education
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Doctor of Philosophy in Mathematics (2024)
University of the Philippines DilimanDissertation: Modularity and arithmetic of certain \(q\)-continued fractions
Adviser: Dr. Victor Manuel R. Aricheta -
Master of Science in Mathematics (2019)
University of the Philippines DilimanThesis: Class invariants from generalized Weber functions of level \(144\)
Adviser: Dr. Richell O. Celeste -
Bachelor of Science in Mathematics (2016)
University of the Philippines DilimanThesis: \(p\)-adic construction of ordinary elliptic curves of a given order
Adviser: Dr. Richell O. Celeste
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Doctor of Philosophy in Mathematics (2024)
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Research
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
Past undergraduate advisees
- Art James Symon Siat (BS Math, Second Semester AY 2024-25)
Past undergraduate co-advisees
- Charles Justin Shi (BS Math, First Semester AY 2024-25, Adviser: Dr. VM Aricheta)
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Teaching
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
Courses Previously Taught
- Math 14
- Math 17
- Math 21, 22, 23
- Math 53, 54
- Math 117
- Math 197
- Math 200
- Math 217
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Publications
Refereed Papers
- A new proof of an identity concerning \(5\)-core partitions, to appear in New Zealand J. Math.
- Ramanujan’s continued fractions of order \(10\) as modular functions (with VM Aricheta), J. Number Theory 278 (2026), 214-244.
- Asymptotic formulas for some \(3\)-color partitions, to appear in J. Anal.
- A remark on generalised cubic partitions modulo \(5\), Bull. Aust. Math. Soc. (2025)
- Modularity of certain products of the cubic continued fraction, J. Korean Math. Soc. 62 (2025), 537-556.
- 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.
- A note on congruences for generalized cubic partitions modulo primes, Integers 25 (2025), paper no. A20, 5 pp.
- Analogue of Ramanujan’s function \(k(\tau)\) for the continued fraction \(X(\tau)\) of order six (with VM Aricheta), Ann. Univ. Ferrara Sez. VII Sci. Mat. 71 (2025), paper no. 6, 18 pp.
- A note on the exact formulas for certain \(2\)-color partitions, C. R. Math. Acad. Sci. Paris 362 (2024), 1485-1490.
- Modularity of a certain continued fraction of Ramanujan, Ramanujan J. 63 (2024), 947-967.
- Modularity of generalized Weber functions \(v_{l,k,N/l}\) (with R Celeste), Matimyas Mat. 45 (2022), 1-12.
Preprints
- The \(k\)-elongated plane partition function modulo small powers of \(5\)
- Remarks on a certain restricted partition function of Lin
- New Gosper’s Lambert series identities of levels \(12\) and \(16\)
- Gosper’s Lambert series identities of level \(14\)
- A remark on modular equations involving Rogers-Ramanujan continued fraction via 5-dissections
- Modularity of certain products of the Rogers-Ramanujan continued fraction
For preprints before 2024, please visit this arXiV link.