CM values of higher automorphic Green functions for orthogonal groups
Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the
automorphic Green function G_s (z_1, z_2) G s (z 1, z 2) for the elliptic modular group at …
automorphic Green function G_s (z_1, z_2) G s (z 1, z 2) for the elliptic modular group at …
Singular units and isogenies between CM elliptic curves
Y Li - Compositio Mathematica, 2021 - cambridge.org
Singular units and isogenies between CM elliptic curves Page 1 Singular units and
isogenies between CM elliptic curves Yingkun Li Compositio Math. 157 (2021), 1022–1035 …
isogenies between CM elliptic curves Yingkun Li Compositio Math. 157 (2021), 1022–1035 …
Algebraicity of higher Green functions at a CM point
Y Li - Inventiones mathematicae, 2023 - Springer
In this paper, we investigate the algebraic nature of the value of a higher Green function on
an orthogonal Shimura variety at a single CM point. This is motivated by a conjecture of …
an orthogonal Shimura variety at a single CM point. This is motivated by a conjecture of …
Almost a century of answering the question: what is a mock theta function
W Duke - Notices of the AMS, 2014 - ams.org
Quite a few famous and extraordinarily gifted mathematicians led lives that were tragically
cut short. Ramanujan is certainly among them. While suffering from a fatal disease, he …
cut short. Ramanujan is certainly among them. While suffering from a fatal disease, he …
Average CM-values of higher Green's function and factorization
Y Li - American Journal of Mathematics, 2022 - muse.jhu.edu
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 …
Zagier concerning the values of higher Green's function at CM points. Furthermore, we give …
Harmonic Maass forms of weight
W Duke, Y Li - 2015 - projecteuclid.org
The object of this paper is to initiate a study of the Fourier coefficients of a weight 1 harmonic
Maass form and relate them to the complex Galois representation associated to a weight 1 …
Maass form and relate them to the complex Galois representation associated to a weight 1 …
Petersson inner products of weight-one modular forms
M Viazovska - Journal für die reine und angewandte Mathematik …, 2019 - degruyter.com
In this paper we study the regularized Petersson product between a holomorphic theta
series associated to a positive definite binary quadratic form and a weakly holomorphic …
series associated to a positive definite binary quadratic form and a weakly holomorphic …
Regularized inner products of meromorphic modular forms and higher Green's functions
K Bringmann, B Kane… - Communications in …, 2019 - World Scientific
In this paper, we study generalizations of Poincaré series arising from quadratic forms,
which naturally occur as outputs of theta lifts. Integrating against them yields evaluations of …
which naturally occur as outputs of theta lifts. Integrating against them yields evaluations of …
Special values of Green's functions on hyperbolic -space
S Herrero, Ö Imamoglu, AM von Pippich… - arXiv preprint arXiv …, 2024 - arxiv.org
Gross, Kohnen and Zagier proved an averaged version of the algebraicity conjecture for
special values of higher Green's functions on modular curves. In this work, we study an …
special values of higher Green's functions on modular curves. In this work, we study an …
Kontsevich–Zagier integrals for automorphic Green's functions. I
Y Zhou - The Ramanujan Journal, 2015 - Springer
In the framework of Kontsevich–Zagier periods, we derive integral representations for weight-
k automorphic Green's functions invariant under modular transformations in\varGamma _0 …
k automorphic Green's functions invariant under modular transformations in\varGamma _0 …