On a Zeta Function Associated to a Quadratic Order

Ye, Dongxi

doi:10.1007/s00025-019-1153-1

Results Math

2020

DOI: 10.1007/s00025-019-1153-1

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On a Zeta Function Associated to a Quadratic Order

Dongxi Ye

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Cited by 2 publications

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“…dition (2.3), p. 237] since for such cases, j p (τ) are uniformizers for X 0 (p).Proofs of the following lemmas can be found in[20, Corollaries 3.1 and 3.…”

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confidence: 96%

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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“…dition (2.3), p. 237] since for such cases, j p (τ) are uniformizers for X 0 (p).Proofs of the following lemmas can be found in[20, Corollaries 3.1 and 3.…”

mentioning

confidence: 96%

On a conjecture of Chen and Yui: Resultants and discriminants

Ye¹

2020

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

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On a conjecture of Chen and Yui: Fricke groups

2023

Journal of Number Theory

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On a Zeta Function Associated to a Quadratic Order

Cited by 2 publications

References 8 publications

On a conjecture of Chen and Yui: Resultants and discriminants

On a conjecture of Chen and Yui: Resultants and discriminants

On a conjecture of Chen and Yui: Fricke groups

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