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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arithmetic mixed Siegel-Weil formulas and modular forms of arithmetic divisors
算术混合 西格尔-威尔公式 算术除数 模形式
2023/5/5
The classical Siegel–Weil formula relates theta series to Eisenstein series and its arithmetic version is central in Kudla's program. I will discuss arithmetic mixed Siegel-Weil formulas. I will focus...
SPECTACLE CYCLES WITH COEFFICIENTS AND MODULAR FORMS OF HALF-INTEGRAL WEIGHT
SPECTACLE CYCLES COEFFICIENTS AND MODULAR FORMS HALF-INTEGRAL WEIGHT
2015/10/14
In this paper we present a geometric way to extend the Shintani lift from even weight cusp forms for congruence subgroups to arbitrary modular forms, in particular Eisenstein series. This is part of o...
CYCLES WITH LOCAL COEFFICIENTS FOR ORTHOGONAL GROUPS AND VECTOR-VALUED SIEGEL MODULAR FORMS
CYCLES WITH LOCAL COEFFICIENTS ORTHOGONAL GROUPS VECTOR-VALUED SIEGEL MODULAR FORMS
2015/10/14
The purpose of this paper is to generalize the relation between intersection numbers of cycles in locally symmetric spaces of orthogonal type and Fourier coefficients of Siegel modular forms to the ca...
MODULAR FORMS AND SOME CASES OF THE INVERSE GALOIS PROBLEM
MODULAR FORMS SOME CASES INVERSE GALOIS PROBLEM
2015/8/26
We prove new cases of the inverse Galois problem by considering the residual Galois representations arising from a fixed newform. Specific choices of weight 3 newforms will show thatthere are Galois e...
Let F be a real quadratic field with ring of integers O and with class number 1. Let Γ be a congruence subgroup of GL2 (O)GL2() . We describe a technique to compute the action of the Hecke operators o...
Modular forms and elliptic curves over the field of fifth roots of unity
Cyclotomic field unity modular elliptic curve
2014/12/24
Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity of elliptic curves over F
A note on modular forms and generalized anomaly cancellation formulas
Modular invariance Anomaly cancellation formulas
2018/4/19
By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formulasKe...
Linear Mahler Measures and Double L-values of Modular Forms
Linear Mahler Measures Double L-values of Modular Forms Number Theory
2012/6/27
We consider the Mahler measure of the polynomial 1+x_1+x_2+x_3+x_4, which is the first case not yet evaluated explicitly. A conjecture due to F. Rodriguez-Villegas represents this Mahler measure as a ...
Eichler Cohomology of Generalized Modular Forms of Real Weights
Eichler Cohomology Generalized Modular Forms Number Theory
2012/5/9
In this paper, we prove the Eichler cohomology theorem of weakly parabolic generalized modular forms of real weights on subgroups of finite index in the full modular group. We explicitly establish the...
Computing power series expansions of modular forms
power series expansions of modular forms Number Theory
2012/5/9
We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.
On the Petersson scalar product of arbitrary modular forms
Petersson scalar product arbitrary modular forms Number Theory
2012/4/18
We consider a natural extension of the Petersson scalar product to the entire space of modular forms of integral weight $k\ge 2$ for a finite index subgroup of the modular group. We show that Hecke op...
Ramanujan type congruences for modular forms of several variables
Congruences for modular forms Cusp forms Number Theory
2012/4/17
We give congruences between the Eisenstein series and a cusp form in the cases of Siegel modular forms and Hermitian modular forms. We should emphasize that there is a relation between the existence o...
A note on modular forms and generalized anomaly cancellation formulas
Modular invariance Anomaly cancellation formulas
2018/4/19
By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formulas
Modular forms and generalized anomaly cancellation formulas
Modular forms generalized anomaly cancellation formulas
2018/4/19
In this paper, we generalize the anomaly cancellation formulas in [1, 12, 7] to the cases that an auxiliary bundle W as well as a complex line bundle are involved with no conditions on the first Pon...
Quasi-modular forms attached to Hodge structures
Polarized Hodge structure Griffiths transversality
2010/12/13
The space D of Hodge structures on a fixed polarized lattice is known as Griffiths period domain and its quotient by the isometry group of the lattice is the moduli of polarized Hodge structures of a ...