Chi-Yun Hsu

University of California, Los Angeles | UCLA · Department of Mathematics

Let $E/\mathbf{Q}$ be an elliptic curve and let $p$ be an odd prime of good reduction for $E$. Let $K$ be an imaginary quadratic field satisfying the classical Heegner hypothesis and in which $p$ splits. In a previous work, Agboola--Castella formulated an analogue of the Birch--Swinnerton-Dyer conjecture for the $p$-adic $L$-function $L_{\mathfrak{...

Euler's identity equates the number of partitions of any non-negative integer n into odd parts and the number of partitions of n into distinct parts. Beck conjectured and Andrews proved the following companion to Euler's identity: the excess of the number of parts in all partitions of n into odd parts over the number of parts in all partitions of n...

Let F be a totally real field and p a rational prime unramified in F. We prove a partial classicality theorem for overconvergent Hilbert modular forms: when the slope is small compared to a subset of weights, an overconvergent form is partially classical. We use the method of analytic continuation.

In this paper we add to the literature on the combinatorial nature of the mock theta functions, a collection of curious $q$-hypergeometric series introduced by Ramanujan in his last letter to Hardy in 1920, which we now know to be important examples of mock modular forms. Our work is inspired by Beck's conjecture, now a theorem of Andrews, related...

Let F be a totally real field and p a rational prime unramified in F. We prove a partial classicality theorem for overconvergent Hilbert modular forms: when the slope is small compared to certain but not all weights, an overconvergent form is partially classical. We use the method of analytic continuation.

Euler's identity equates the number of partitions of any non-negative integer n into odd parts and the number of partitions of n into distinct parts. Beck conjectured and Andrews proved the following companion to Euler's identity: the excess of the number of parts in all partitions of n into odd parts over the number of parts in all partitions of n...

For a non-endoscopic cohomological cuspidal automorphic representation of $\mathrm{GSp}_4 \times \mathrm{GL}_2$, assumed to be $p$-ordinary, we construct an Euler system for the Galois representation associated to it. Both the construction and the verification of tame norm relations are based on Novodvorsky's integral formula for the $L$-function o...

Let f be a modular form with complex multiplication. If f has critical slope, then Coleman's classicality theorem implies that there is a p-adic overconvergent generalized Hecke eigenform with the same Hecke eigenvalues as f. We give a formula for the Fourier coefficiets of this generalized Hecke eigenform. We also investigate the dimension of the...

Let [Formula: see text] be a modular form with complex multiplication. If [Formula: see text] has critical slope, then Coleman’s classicality theorem implies that there is a [Formula: see text]-adic overconvergent generalized Hecke eigenform with the same Hecke eigenvalues as [Formula: see text]. We give a formula for the Fourier coefficients of th...

Andreatta-Iovita-Pilloni constructed eigenvarieties for cuspidal Hilbert modular forms. The eigenvariety has a natural map to the weight space, called the weight map. At a classical point, we compute a lower bound of the dimension of the tangent space of the fiber of the weight map using Galois deformation theory. Along with the classicality theore...

We show that the compactly supported cohomology of certain $\mathrm{U}(n,n)$ or $\mathrm{Sp}(2n)$-Shimura varieties with $\Gamma_1(p^\infty)$-level vanishes above the middle degree. The only assumption is that we work over a CM field $F$ in which the prime $p$ splits completely. We also give an application to Galois representations for torsion in t...

A strong edge-coloring of a graph is a function that assigns to each edge a color such that two edges within distance two apart receive different colors. The strong chromatic index of a graph is the minimum number of colors used in a strong edge-coloring. This paper determines strong chromatic indices of cacti, which are graphs whose blocks are cyc...