Bo-Hae Im

activity

20032026

most citedAbelian Varieties and Finitely Generated Galois Groups

2 citations · 10 across the 30 of their papers we have counts for

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27 papers · 1 filter

math.NT2026

The threshold for linear independence of multiple zeta values in positive characteristic

Bo-Hae Im, Hojin Kim, Tuan Ngo Dac

A fundamental conjecture formulated by Thakur in 2009, which has guided significant developments in function field arithmetic, asserts that multiple zeta values (MZV's) in positive…

math.NT2023

Growth of Torsion Groups of Elliptic Curves Over Number Fields without Rationally Defined CM

Bo-Hae Im, Hansol Kim

For a quadratic field $K$ without rationally defined CM, we prove that there exists of a prime $p_{K}$ depending only on $K$ such that if $d$ is a pos…

math.NT2023

Hopf algebras and alternating multiple zeta values in positive characteristic

Bo-Hae Im, Hojin Kim, Khac Nhuan Le +2

In \cite{IKLNDP23} we presented a systematic study of algebra structures of multiple zeta values in positive characteristic introduced by Thakur as analogues of classical multiple…

math.NT2023★ 1 cited

Hopf algebras and multiple zeta values in positive characteristic

Bo-Hae Im, Hojin Kim, Khac Nhuan Le +2

Multiples zeta values (MZV's for short) in positive characteristic were introduced by Thakur as analogues of classical multiple zeta values of Euler. In this paper we give a system…

math.NT2022

Density of Elliptic Curves over Number Fields with Prescribed Torsion Subgroups

Bo-Hae Im, Hansol Kim

Let $K$ be a number field. For positive integers $m$ and $n$ such that $m ∣ n$ , we let $S_{m, n}$ be the set of elliptic curves $E / K$ defined over $K$ such that $E(K)_{\…

math.NT2022

Non-holomorphic Eisenstein series for certain Fuchsian groups and class numbers

Bo-Hae Im, Wonwoong Lee

We study certain types of Fuchsian groups of the first kind denoted by $R (N)$ , which coincide with the Fricke groups or the arithmetic Hecke triangle groups of low levels. We find…

math.NT2022

On the common zeros of quasi-modular forms for $Γ_{0}^{+} (N)$ of level $N = 1, 2, 3$

Bo-Hae Im, Hojin Kim, Wonwoong Lee

In this paper, we study common zeros of the iterated derivatives of the Eisenstein series for $Γ_{0}^{+} (N)$ of level $N = 1, 2$ and $3$ , which are quasi-modular forms. More precisely, we…

math.NT2022

Zagier-Hoffman's conjectures in positive characteristic

Bo-Hae Im, Hojin Kim, Khac Nhuan Le +2

Multiples zeta values and alternating multiple zeta values in positive characteristic were introduced by Thakur and Harada as analogues of classical multiple zeta values of Euler a…

math.NT2021

Rank gain of Jacobians over number field extensions with prescribed Galois groups

Bo-Hae Im, Joachim König

We investigate the rank gain of elliptic curves, and more generally, Jacobian varieties, over non-Galois extensions whose Galois closure has Galois group permutation-isomorphic to…

math.NT2020

A classification of the automorphism groups of polarized abelian threefolds over finite fields

WonTae Hwang, Bo-Hae Im, Hansol Kim

We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.

math.NT2019★ 2 cited

Abelian Varieties and Finitely Generated Galois Groups

Bo-Hae Im, Michael Larsen

This paper surveys the methods that have been used to attack the conjecture, still open, that an abelian variety over a characteristic $0$ field with finitely generated Galois grou…

math.NT2018★ 1 cited

Waring's problem for rational functions in one variable

Bo-Hae Im, Michael Larsen

Let $f \in Q (x)$ be a non-constant rational function. We consider "Waring's Problem for $f (x)$ ," i.e., whether every element of $\bbq$ can be written as a bounded sum of el…

math.NT2017★ 1 cited

Ranks of rational points of the Jacobian varieties of hyperelliptic curves

Bo-Hae Im, Byoung Du Kim

In this paper, we obtain bounds for the Mordell-Weil ranks over cyclotomic extensions of a wide range of abelian varieties defined over a number field $F$ whose primes above $p$ ar…

math.NT2015

Notes on Weierstrass points of modular curves $X_{0} (N)$

Bo-Hae Im, Daeyeol Jeon, Chang Heon Kim

We give conditions when the fixed points by the partial Atkin-Lehner involutions on $X_{0} (N)$ are Weierstrass points as an extension of the result by Lehner and Newman \cite{LN}. Fu…

math.NT2015

Rank gain of Jacobians over finite Galois extensions

Bo-Hae Im, Erik Wallace

Let $X$ be a Riemann surface of genus $g > 0$ defined over a number field $K$ which is a degree $d$ -covering of $P_{K}^{1}$ . In this paper we show the existence of inf…

math.NT2012

Infinite rank of elliptic curves over $\mathbf{Q}^{\ab}$

Bo-Hae Im, Michael Larsen

If $E$ is an elliptic curve defined over a quadratic field $K$ , and the $j$ -invariant of $E$ is not 0 or 1728, then $E(\mathbf{Q}^{\ab})$ has infinite rank. If $E$ is an elliptic c…

math.NT2012

Some Applications of the Hales-Jewett Theorem to Field Arithmetic

Bo-Hae Im, Michael Larsen

Let $K$ be a field whose absolute Galois group is finitely generated. If $K$ neither finite nor of characteristic 2, then every hyperelliptic curve over $K$ with all of its Weierst…

math.NT2010

Parallelopipeds of Positive Rank Twists of Elliptic Curves

Bo-Hae Im, Michael Larsen

For every n there exists an elliptic curve E over the rational numbers and an n-dimensional subspace V of non-zero rationals modulo squares such that for all v in V, the quadratic…

math.NT2009

Semi-direct Galois covers of the affine line

Linda Gruendken, Laura Hall-Seelig, Bo-Hae Im +3

Let $k$ be an algebraically closed field of characteristic $p > 0$ . Let $G$ be $Z / ℓ Z$ semi-direct product $Z / pZ$ where $ℓ$ is a prime distinct from $p$ . In this paper, we stud…

math.NT2008

A Weak Chevalley-Warning Theorem for Quasi-finite Fields

Michael Larsen, Bo-Hae Im

There exists a function f: N -> N such that for every positive integer d, every quasi-finite field K and every projective hypersurface X of degree d and dimension at least f(d), th…

math.NT2006

Abelian Varieties over Cyclic Fields

Bo-Hae Im, Michael Larsen

Let K be a field not of characteristic 2 such that every finite separable extension of K is cyclic. Let A be an abelian variety over K. If K is infinite, then A(K) is Zariski-dense…

math.NT2006

Heegner points and the rank of elliptic curves over large extensions of global fields

Florian Breuer, Bo-Hae Im

Let k be a global field, $k ˉ$ a separable closure of k, and $G_{k}$ the absolute Galois group $\Gal(\bar{k}/k)$ of $k ˉ$ over k. For every g in $G_{k}$ , let $k ˉ^{g}$ be the…

math.NT2005

Open conditions for infinite multiplicity eigenvalues on elliptic curves

Bo-Hae Im, Michael Larsen

Let E be an elliptic curve defined over a number field K, V the complexification of the group of rational points of E over an algebraic closure L of K, and G the Galois group Gal(L…

math.NT2004★ 1 cited

Heegner points and Mordell-Weil groups of elliptic curves over large fields

Bo-Hae Im

Let $E/\bbq$ be an elliptic curve defined over $\bbq$ with conductor $N$ and $\gq$ the absolute Galois group of an algebraic closure $\bar{\bbq}$ of $\bbq$. We prove that for every…

The threshold for linear independence of multiple zeta values in positive characteristic

Growth of Torsion Groups of Elliptic Curves Over Number Fields without Rationally Defined CM

Hopf algebras and alternating multiple zeta values in positive characteristic

Hopf algebras and multiple zeta values in positive characteristic

Density of Elliptic Curves over Number Fields with Prescribed Torsion Subgroups

Non-holomorphic Eisenstein series for certain Fuchsian groups and class numbers

On the common zeros of quasi-modular forms for Γ0+​(N) of level N=1,2,3

Zagier-Hoffman's conjectures in positive characteristic

Rank gain of Jacobians over number field extensions with prescribed Galois groups

A classification of the automorphism groups of polarized abelian threefolds over finite fields

Abelian Varieties and Finitely Generated Galois Groups

Waring's problem for rational functions in one variable

Ranks of rational points of the Jacobian varieties of hyperelliptic curves

Notes on Weierstrass points of modular curves X0​(N)

Rank gain of Jacobians over finite Galois extensions

Infinite rank of elliptic curves over $\mathbf{Q}^{\ab}$

Some Applications of the Hales-Jewett Theorem to Field Arithmetic

Parallelopipeds of Positive Rank Twists of Elliptic Curves

Semi-direct Galois covers of the affine line

A Weak Chevalley-Warning Theorem for Quasi-finite Fields

Abelian Varieties over Cyclic Fields

Heegner points and the rank of elliptic curves over large extensions of global fields

Open conditions for infinite multiplicity eigenvalues on elliptic curves

Heegner points and Mordell-Weil groups of elliptic curves over large fields

On the common zeros of quasi-modular forms for $Γ_{0}^{+} (N)$ of level $N = 1, 2, 3$

Notes on Weierstrass points of modular curves $X_{0} (N)$