Kenny Lau

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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.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.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…

Local Factors in the BSD Conjecture: A Unified Statistical View

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

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

Almost all primes are partially regular

Parity of k-differentials in genus zero and one

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