arXiv subjects

Hae-Sang Sun

Publications and source records attributed to Hae-Sang Sun.

5 recordsLinked to original sources

arXiv2024

Cyclotomic fields are generated by cyclotomic Hecke {\it L}-values of totally real fields, II

Jun-Lee-Sun posed the question of whether the cyclotomic Hecke field can be generated by a single critical $L$-value of a cyclotomic Hecke character over a totally real field. They provided an answer to this question in the case where the tame Hecke character is trivial. In this paper, we extend their work to address the case of non-trivial Hecke characters over solvable totally real number fields. Our approach builds upon the primary estimation obtained by Jun-Lee-Sun, supplemented with new inputs, including global class field theory, duality principles, the analytic behavior of partial Hecke $L$-functions, and the non-vanishing of twisted Gauss sums and Hyper Kloosterman sums.

math.NT↗

arXiv2021

Non-vanishing of special $L$-values of cusp forms on GL(2) with totally split prime power twists

We prove the non-vanishing of special $L$-values of cuspidal automorphic forms on GL(2) twisted by Hecke characters of prime power orders and totally split prime power conductors. Main ingredients of the proof are estimating the Galois averages of fast convergent series expressions of special $L$-values and considering Shintani cone decomposition.

math.NT↗

arXiv2020

On the indivisibility of derived Kato's Euler systems and the main conjecture for modular forms

We provide a simple and efficient numerical criterion to verify the Iwasawa main conjecture and the indivisibility of derived Kato's Euler systems for modular forms of weight two at any good prime under mild assumptions. In the ordinary case, the criterion works for all members of a Hida family once and for all. The key ingredient is the explicit computation of the integral image of the derived Kato's Euler systems under the dual exponential map. We provide explicit new examples at the end. This work does not appeal to the Eisenstein congruence method at all.

math.NT↗

arXiv2019

Dynamics of continued fractions and distribution of modular symbols

We formulate a thermodynamical approach to the study of distribution of modular symbols, motivated by the work of Baladi-Vall\'ee. We introduce the modular partitions of continued fractions and observe that the statistics for modular symbols follow from the behavior of modular partitions. We prove the limit Gaussian distribution and residual equidistribution for modular partitions as a vector-valued random variable on the set of rationals whose denominators are up to a fixed positive integer by studying the spectral properties of transfer operator associated to the underlying dynamics. The approach leads to a few applications. We show an average version of conjectures of Mazur-Rubin on statistics for the period integrals of an elliptic newform. We further observe that the equidistribution of mod $p$ values of modular symbols leads to mod $p$ non-vanishing results for special modular $L$-values twisted by a Dirichlet character.

math.NT↗

arXiv2013

Distance sets of two subsets of vector spaces over finite fields

We investigate the size of the distance set determined by two subsets of finite dimensional vector spaces over finite fields. A lower bound of the size is given explicitly in terms of cardinalities of the two subsets. As a result, we improve upon the results by Rainer Dietmann. In the case that one of the subsets is a product set, we obtain further improvement on the estimate.

math.CO↗