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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...
THE GEOMETRIC THETA CORRESPONDENCE FOR HILBERT MODULAR SURFACES
GEOMETRIC THETA CORRESPONDENCE；HILBERT MODULAR SURFACES
2015/10/14
In a series of papers [11, 12, 13, 14] we have been studying the geometric theta correspondence (see below) for non-compact arithmetic quotients of symmetric spaces associated to orthogonal groups. It...
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...
The modular group action on real SL(2){characters of a one-holed torus
one-holed torus group action
2015/9/29
The
action of Γ preserves a Poisson structure de ning a Γ{invariant area form on each
−1(t)\ R3. For t < 2, the action of Γ is properly discontinuous on the four contractible components of &...
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...
The modular ocean data assimilation system (MODAS) was designed to meet the U.S. Navy's need to produce rapid estimates of present and near-term ocean conditions, often in situations where little or n...
The aim of this paper is to give a purely rigid-analytic development of the theory of canonical subgroups
with arbitrary torsion-level in generalized elliptic curves over rigid spaces over k (using L...
MODULAR CURVES AND RAMANUJAN’S CONTINUED FRACTION
modular curve Ramanujan continued fraction
2015/7/6
We use arithmetic models of modular curves to establish some properties of Ramanujan’s continued fraction. In particular, we give a new geometric proof that its singular values are algebraic units
th...
ERRATUM TO MODULAR CURVES AND RAMANUJAN’S CONTINUED FRACTION
q-series modular curve Ramanujan continued fraction
2015/7/6
This lemma is already false for k = p quite generally, and our error in the proof of the
lemma occurs in the line beginning “Evidently. . . ” (the formula given for (k, m+jk/p)
in that line is wrong...
Liouville theory is characterized by the exponential interaction μe2bφ and a coupling to worldsheet curvature QRφ. A typical irrational CFT (c = 1 + 6Q2). Difficult theory solved in late 90’s using th...
Description and implementation of a MiXed Layer model (MXL, v1.0) for the dynamics of the atmospheric boundary layer in the Modular Earth Submodel System (MESSy)
Description and implementation MiXed Layer model
2015/3/5
We present a new submodel for the Modular Earth
Submodel System (MESSy): the MiXed Layer (MXL) model
for the diurnal dynamics of the convective boundary layer,
including explicit representations of...
MOMBA 1.1 – a high-resolution Baltic Sea configuration of GFDL's Modular Ocean Model
high-resolution Baltic Sea configuration GFDL Modular Ocean Model
2014/12/19
We present a new coupled ocean-circulation–ice model configuration of the Baltic Sea. The model features, contrary to most existing configurations, a high horizontal resolution of ≈ 1 nautical ...
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 ...