Junehyuk Jung

activity

20112025

most citedQuantitative quantum ergodicity and the nodal domains of Maass-Hecke cusp forms

8 citations · 20 across the 12 of their papers we have counts for

collaborators

19 papers

math.NT2025

Linnik problem for Maass--Hecke cuspforms and effective multiplicity one theorem

Junehyuk Jung, Min Lee

We investigate two related problems concerning the dimension of joint eigenspaces of the Laplace--Beltrami operator and a finite set of Hecke operators on $\mathbb{X}=\mathrm{PGL}_…

math.SP2022

$2$ -nodal domain theorems for higher dimensional circle bundles

Junehyuk Jung, Steve Zelditch

We prove that the real parts of equivariant (but non-invariant) eigenfunctions of generic bundle metrics on nontrivial principal $S^{1}$ bundles over manifolds of any dimension have…

math.NT2021★ 1 cited

Non-vanishing of symmetric cube $L$ -functions

Jeff Hoffstein, Junehyuk Jung, Min Lee

We prove that there are infinitely many Maass--Hecke cuspforms over the field $Q [- 3]$ such that the corresponding symmetric cube $L$ -series does not vanish at the c…

math.NT2021

Intersecting geodesics on the modular surface

Junehyuk Jung, Naser Talebizadeh Sardari

We introduce the \textit{modular intersection kernel}, and we use it to study how geodesics intersect on the full modular surface $\mathbb{X}=PSL_2\left(\mathbb{Z}\right) \backslas…

math.NT2020

Embedding closed totally geodesic surfaces in Bianchi orbifolds

Junehyuk Jung, Alan W. Reid

We study embedding of closed totally geodesic hyperbolic 2-orbifolds in the Bianchi orbifolds $H^{3} / P S L (2, O_{d})$ . Our main result shows that there is a constant $c…

math.DG2019★ 3 cited

Topology of the nodal set of random equivariant spherical harmonics on $S^{3}$

Junehyuk Jung, Steve Zelditch

We show that real and imaginary parts of equivariant spherical harmonics on $S^{3}$ have almost surely a single nodal component. Moreover, if the degree of the spherical harmonic is…

math.NT2018

Asymptotic trace formula for the Hecke operators

Junehyuk Jung, Simon Marshall, Naser T. Sardari

Given integers $m$ , $n$ and $k$ , we give an explicit formula with an optimal error term (with square root cancelation) for the Petersson trace formula involving the $m$ -th and $n$ -…

math.SP2018

Boundedness of the number of nodal domains for eigenfunctions of generic Kaluza-Klein $3$ -folds

Junehyuk Jung, Steve Zelditch

This article concerns the number of nodal domains of eigenfunctions of the Laplacian on special Riemannian $3$ -manifolds, namely nontrivial principal $S^{1}$ bundles $P \to X$ over R…

math.NT2018

On the growth of the number of totally geodesic surfaces in some hyperbolic $3$ -manifolds

Junehyuk Jung

Let $d$ be a positive square-free integer $\equiv 3 (mod 4)$ such that there is no invariant of the ideal class group $Q [- d]$ which is divisible by $4…

math.SP2017

Bounding the number of nodal domains of eigenfunctions without singular points on the square

Junehyuk Jung

We prove Polterovich's conjecture concerning the growth of the number of nodal domains for eigenfunctions on a unit square domain, under the assumption that the eigenfunctions do n…

math.NT2016★ 1 cited

Sign changes of the Eisenstein series on the critical line

Junehyuk Jung, Matthew P. Young

We prove a quantitative lower bound on the number of nodal domains of the real-analytic Eisenstein series. The main tool in the proof is a quantitative restricted QUE theorem where…

math.CO2016

On tiling the integers with $4$ -sets of the same gap sequence

Ilkyoo Choi, Junehyuk Jung, Minki Kim

Partitioning a set into similar, if not, identical, parts is a fundamental research topic in combinatorics. The question of partitioning the integers in various ways has been consi…

math.SP2015

Quantum unique ergodicity and the number of nodal domains of eigenfunctions

Seung Uk Jang, Junehyuk Jung

We prove that the Hecke--Maass eigenforms for a compact arithmetic triangle group have a growing number of nodal domains as the eigenvalue tends to $+ \infty$ . More generally the sa…

math.SP2014★ 5 cited

Number of nodal domains of eigenfunctions on non-positively curved surfaces with concave boundary

Junehyuk Jung, Steve Zelditch

It is an open problem in general to prove that there exists a sequence of $Δ_{g}$ -eigenfunctions $ϕ_{j_{k}}$ on a Riemannian manifold $(M, g)$ for which the number $N (ϕ_{j_{k}})$ of nod…

math.SP2013

Number of nodal domains and singular points of eigenfunctions of negatively curved surfaces with an isometric involution

Junehyuk Jung, Steve Zelditch

We prove two types of nodal results for density one subsequences of an orthonormal basis ${ϕ_{j}}$ of eigenfunctions of the Laplacian on a negatively curved compact surface. The fi…

math.NT2013★ 8 cited

Quantitative quantum ergodicity and the nodal domains of Maass-Hecke cusp forms

Junehyuk Jung

We prove a quantitative statement of the quantum ergodicity for Hecke--Maass cusp forms on the modular surface. As an application of our result, along a density $1$ subsequence of…

math.NT2012★ 2 cited

On sparsity of positive-definite automorphic forms within a family

Junehyuk Jung

It is known due to Baker and Montgomery that almost all Fekete polynomials under certain ordering have at least one zero on the interval (0, 1). In terms of the positive-definitene…

math.NT2011

Pretentiously detecting power cancellation

Junehyuk Jung, Robert J. Lemke Oliver

Granville and Soundararajan have recently introduced the notion of pretentiousness in the study of multiplicative functions of modulus bounded by 1, essentially the idea that two f…

math.DG2011

Sharp bounds for the intersection of nodal lines with certain curves

Junehyuk Jung

Let $Y$ be a hyperbolic surface and let $ϕ$ be a Laplacian eigenfunction having eigenvalue $- 1/4 - τ^{2}$ with $τ > 0$ . Let $N (ϕ)$ be the set of nodal lines of $ϕ$ . For a fixed analytic…

Linnik problem for Maass--Hecke cuspforms and effective multiplicity one theorem

2-nodal domain theorems for higher dimensional circle bundles

Non-vanishing of symmetric cube L-functions

Intersecting geodesics on the modular surface

Embedding closed totally geodesic surfaces in Bianchi orbifolds

Topology of the nodal set of random equivariant spherical harmonics on S3

Asymptotic trace formula for the Hecke operators

Boundedness of the number of nodal domains for eigenfunctions of generic Kaluza-Klein 3-folds

On the growth of the number of totally geodesic surfaces in some hyperbolic 3-manifolds

Bounding the number of nodal domains of eigenfunctions without singular points on the square

Sign changes of the Eisenstein series on the critical line

On tiling the integers with 4-sets of the same gap sequence

Quantum unique ergodicity and the number of nodal domains of eigenfunctions

Number of nodal domains of eigenfunctions on non-positively curved surfaces with concave boundary

Number of nodal domains and singular points of eigenfunctions of negatively curved surfaces with an isometric involution

Quantitative quantum ergodicity and the nodal domains of Maass-Hecke cusp forms

On sparsity of positive-definite automorphic forms within a family

Pretentiously detecting power cancellation

Sharp bounds for the intersection of nodal lines with certain curves

$2$ -nodal domain theorems for higher dimensional circle bundles

Non-vanishing of symmetric cube $L$ -functions

Topology of the nodal set of random equivariant spherical harmonics on $S^{3}$

Boundedness of the number of nodal domains for eigenfunctions of generic Kaluza-Klein $3$ -folds

On the growth of the number of totally geodesic surfaces in some hyperbolic $3$ -manifolds

On tiling the integers with $4$ -sets of the same gap sequence