arXiv subjects
Publications and source records attributed to Dongxi Ye.
In this work, we derive Gross-Zagier type CM value formulas for Hauptmoduls $j_{p}^{*}(τ)$ on Fricke groups $Γ_{0}^{*}(p)$. We also illustrate how to employ these formulas to obtain certain Hilbert class polynomials.
In this short note, by modifying the results and proofs given in the author's recent work, we simply show that the difference of a Hauptmodul for any genus zero group $Γ_{0}(N)$ is a Borcherds lift. This work extends Scheithauer's results in a different direction. As a consequence, we derive Monster denominator formula like product expansion for these Hilbert modular forms.
In this short note, we aim to prove that the Fourier coefficients of the modular function $ \frac{η^{24}(τ)}{η^{24}(2τ)} $ possess a sign-change property.
In this note, we establish $Γ_{1}(N)$-analogues for the monster denominator formula.
Suppose $k$ is a positive integer. In this work, we establish formulas for for the number of representations of integers by the quadratic forms $$ x_{1}^{2}+\cdots+x_{k}^{2}+l\left(x_{k+1}^{2}+\cdots+x_{2k}^{2}\right) $$ for $l\in\{2,4\}$.
In this note, we construct canonical bases for the spaces of weakly holomorphic modular forms with poles supported at the cusp $\infty$ for $Γ_{0}(4)$ of integral weight $k$ for $k\leq-1$, and we make use of the basis elements for the case $k=-1$ to construct explicit Borcherds products on unitary group $U(2,1)$.
The Ramanujan--Mordell Theorem for sums of an even number of squares is extended to other quadratic forms and quadratic polynomials.