Kelvin Lam

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20232026

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math.NT2026

Consecutive Rankin-Cohen Bases, Full-Spark Periods, and Divisor-Tau Congruences

Kelvin Lam

For $r \geq 1$ , let $K = 2 r + 14$ and $d = dim S_{K}$ . We prove strict positivity for determinants of Mellin period functionals, yielding a full-spark theorem for periods in a fundamental ha…

math.NT2025

Transcendence and algebraic independence of a family of $p$ -adic valuation generating functions

Kelvin Lam

We show that $T_{p} (z) = \prod_{j = 1}^{\infty} (1 - z^{p^{j}})^{- 1/ p^{j}}$ is transcendental over $Q (z)$ , and establish the transcendence of its values at nonzero algeb…

Consecutive Rankin-Cohen Bases, Full-Spark Periods, and Divisor-Tau Congruences

Transcendence and algebraic independence of a family of p-adic valuation generating functions

Transcendence and algebraic independence of a family of $p$ -adic valuation generating functions