Difference of a Hauptmodul for Γ0(N) and certain Gross-Zagier type CM value formulas

Ye, Dongxi

doi:10.1007/s11425-019-1830-3

Cited by 5 publications

(2 citation statements)

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“…In [21], the author of the present work had shown that the automorphic forms −2 log | j p (z 1 ) − j p (z 2 )| 2 are all Borcherds lifts, and these ultimately motivate us to follow the same idea stated above to extend the Gross-Zagier discriminant formula to the cases for j p (τ). In the proof of Theorem 1.6, we realize the index set of the double sum as a small CM 0-cycle that allows us to apply Schofer's small CM value formula to the associated Borcherds lifts.…”

Section: Remark 13 Recall That Formentioning

confidence: 70%

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On a conjecture of Chen and Yui: Resultants and discriminants

Ye¹

2020

Can. J. Math.-J. Can. Math.

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In [5], Chen and Yui conjectured that Gross–Zagier type formulas may also exist for Thompson series. In this work, we verify Chen and Yui’s conjecture for the cases for Thompson series $j_{p}(\tau )$ for $\Gamma _{0}(p)$ for p prime, and equivalently establish formulas for the prime decomposition of the resultants of two ring class polynomials associated to $j_{p}(\tau )$ and imaginary quadratic fields and the prime decomposition of the discriminant of a ring class polynomial associated to $j_{p}(\tau )$ and an imaginary quadratic field. Our method for tackling Chen and Yui’s conjecture on resultants can be used to give a different proof to a recent result of Yang and Yin. In addition, as an implication, we verify a conjecture recently raised by Yang, Yin, and Yu.

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Section: Remark 13 Recall That Formentioning

confidence: 70%

“…It is worthwhile to remark that Yang and Yin's method [16] may give another proof to our Theorem 1.1, and one may find some related work and ideas in [21].…”

Section: Remark I: a Results Of Yang And Yinmentioning

confidence: 97%