Wei-Lun Tsai

collaborators

5 papers

math.NT2026

Difference of the modular function $ω_{2} (τ)$ , revisited

Wei-Lun Tsai, Dongxi Ye

Adapting the analytic method of Gross and Zagier, Roskam proved a prime-factorization formula for the norm of the difference of two level-two Weber singular moduli. Independently,…

math.NT2026

On the Petersson norm $⟨ θ_{ψ}, θ_{ψ} ⟩$

Wei-Lun Tsai, Dongxi Ye

Let $K$ be an imaginary quadratic field of discriminant~ $- d < - 11$ , and for $ℓ \geq 1$ , let $ψ$ be a Hecke character of $K$ with trivial finite conductor and infinite type~$(2\ell,0…

math.NT2024

Euler-type recurrences for $t$ -color and $t$ -regular partition functions

Tapas Bhowmik, Wei-Lun Tsai, Dongxi Ye

We give Euler-like recursive formulas for the $t$ -colored partition function when $t = 2$ or $t = 3,$ as well as for all $t$ -regular partition functions. In particular, we derive an in…

math.NT2024

The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}{π}$

Mark van Hoeij, Wei-Lun Tsai, Dongxi Ye

In this work, we establish modular parameterizations for two general formulas for $\frac{1}{π}$ that subsume conjectural Ramanujan type formulas due to Z.-W. Sun, which have remained…

math.NT2024

Lucas congruences using modular forms

Frits Beukers, Wei-Lun Tsai, Dongxi Ye

In this work, we prove that many Apéry-like sequences arising from modular forms satisfy the Lucas congruences modulo any prime. As an implication, we completely affirm four conjec…

Difference of the modular function ω2​(τ), revisited

On the Petersson norm ⟨θψ​,θψ​⟩

Euler-type recurrences for t-color and t-regular partition functions

The Modularity of Z.-W. Sun's Conjectural Formulas for π1​

Lucas congruences using modular forms

Difference of the modular function $ω_{2} (τ)$ , revisited

On the Petersson norm $⟨ θ_{ψ}, θ_{ψ} ⟩$

Euler-type recurrences for $t$ -color and $t$ -regular partition functions

The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}{π}$