Kenny Lau

collaborators

11 papers

math.NT2026

Local Factors in the BSD Conjecture: A Unified Statistical View

David Kurniadi Angdinata, Kenny Lau, Ken Ono +2

For elliptic curves $E / Q$ in short Weierstrass form \[ E=E(a_4,a_6): y^2=x^3+a_4x+a_6, \] we derive a multivariable Euler product generating function which encodes the Tam…

math.NT2026

Rogers--Ramanujan identities from the geometry of $X^{a} = Y^{b}$

Yifeng Huang, Kenny Lau, Ken Ono

We prove the conjecture of Huang, Jiang, and Oblomkov (HJO) giving a geometric extension of the Rogers--Ramanujan and Andrews--Gordon identities for every torus-knot singularity $X…

math.CO2026

Zero-free columns in character tables of symmetric groups

Colin Defant, Sidharth Hariharan, Kenny Lau +1

The rows and columns of the character table of the symmetric group $S_{n}$ are both naturally indexed by partitions of $n$ . Let $D (n)$ denote the number of conjugacy classes of $S_{n}$ …

math.NT2026

Algebraic geometric framework of Rogers--Ramanujan identities

Yifeng Huang, Kenny Lau, Ken Ono +1

The Rogers--Ramanujan identities equate a $q$ -series whose exponents are governed by a quadratic form with an infinite product supported on two residue classes modulo~ $5$ . Identiti…

math.NT2026

Formalized $q$ -series: The Rogers-Ramanujan Identities and Beyond

Kenny Lau, Seewoo Lee, Ken Ono

The theory of $q$ -series and basic hypergeometric series plays a crucial role at the intersection of combinatorics, number theory, and representation theory. From the classical par…

math.NT2026

Modularity of Point Counts for the Curves $X^{a} = Y^{b}$ : New Rogers--Ramanujan Identities

Kenny Lau, Ken Ono

For coprime $1 < a < b$ , let $M_{n}^{a, b} (F_{q})$ be the set of commuting pairs of nilpotent $n \times n$ matrices over $F_{q}$ with $X^{a} = Y^{b}$ . Huang, Jiang, and Oblomkov as…

math.NT2026

ABC implies that Ramanujan's tau function misses almost all primes

David Kurniadi Angdinata, Evan Chen, Chris Cummins +21

Lehmer conjectured that Ramanujan's tau-function never vanishes. In a related direction, a folklore conjecture asserts that infinitely many primes arise as absolute values of Raman…

math.CO2026

Dead ends in square-free digit walks

Evan Chen, Chris Cummins, Ben Eltschig +18

We study "dead ends" in square-free digit walks: square-free integers $N$ such that, in base $b$ , every one-digit extension $b N + d$ is non-square-free. In base $10$ , the stochastic…

math.NT2026

Almost all primes are partially regular

Evan Chen, Chris Cummins, Ben Eltschig +18

For odd primes $p$ , we let $K_{p} := Q (ζ_{p})$ be the $p$ th cyclotomic field and let $ω$ denote its Teichmuller character. For $α > 1/2$ , we say that an odd prime $p$ is partially…

math.NT2026

Parity of $k$ -differentials in genus zero and one

Dawei Chen, Evan Chen, Kenny Lau +2

Here we completely determine the spin parity of $k$ -differentials with prescribed zero and pole orders on Riemann surfaces of genus zero and one. This result was previously obtaine…

math.CO2026

Fel's Conjecture on Syzygies of Numerical Semigroups

Evan Chen, Chris Cummins, GSM +18

Let $S = ⟨ d_{1}, \dots, d_{m} ⟩$ be a numerical semigroup and $k [S]$ its semigroup ring. The Hilbert numerator of $k [S]$ determines normalized alternating syzygy power sums $K_…

Local Factors in the BSD Conjecture: A Unified Statistical View

Rogers--Ramanujan identities from the geometry of Xa=Yb

Zero-free columns in character tables of symmetric groups

Algebraic geometric framework of Rogers--Ramanujan identities

Formalized q-series: The Rogers-Ramanujan Identities and Beyond

Modularity of Point Counts for the Curves Xa=Yb: New Rogers--Ramanujan Identities

ABC implies that Ramanujan's tau function misses almost all primes

Dead ends in square-free digit walks

Almost all primes are partially regular

Parity of k-differentials in genus zero and one

Fel's Conjecture on Syzygies of Numerical Semigroups

Rogers--Ramanujan identities from the geometry of $X^{a} = Y^{b}$

Formalized $q$ -series: The Rogers-Ramanujan Identities and Beyond

Modularity of Point Counts for the Curves $X^{a} = Y^{b}$ : New Rogers--Ramanujan Identities

Parity of $k$ -differentials in genus zero and one