Average CM-values of higher Green's function and factorization

Yingkun Li

Type: Article

Publication Date: 2022-10-01

Citations: 7

DOI: https://doi.org/10.1353/ajm.2022.0029

Abstract

In this paper, we prove an averaged version of an algebraicity conjecture of Gross and Zagier concerning the values of higher Green's function at CM points. Furthermore, we give the factorization of the ideal generated by such algebraic value in the spirit of the famous work of Gross and Zagier on singular moduli.

Locations

American Journal of Mathematics - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (19)

Action	Title	Year	Authors
+	Higher Green's functions for modular forms	2008	Anton Mellit
+	On Some Arithmetic Properties of Modular Forms of One and Several Variables	1975	Goro Shimura
+	Heights of Heegner cycles and derivatives of L-series	1997	Shou-Wu Zhang
+	Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms	2013	Jan Hendrik Bruinier Ken Ono
+	ARITHMETIC TRACES OF NON-HOLOMORPHIC MODULAR INVARIANTS	2010	Alison Beth Miller Aaron Pixton
+ PDF Chat	Intersection numbers of cycles on locally symmetric spaces and fourier coefficients of holomorphic modular forms in several complex variables	1990	Stephen S. Kudla John J. Millson
+	Heegner points and derivatives ofL-series. II	1987	Benedict H. Gross Winfried Kohnen Don Zagier
+	Central Derivatives of Eisenstein Series and Height Pairings	1997	Stephen S. Kudla
+	Special Values of Green Functions at Big CM Points	2011	Jan Hendrik Bruinier Stephen S. Kudla Tai Yang
+	On the Weil-Siegel formula.	1988	Stephen S. Kudla Stephen Rallis