Ken Ono

works on

alternating permutations 1 dyson rank 1 elliptic functions 1 Euler numbers 1 formal verification 1 lean proof assistant 1 mock modular forms 1 modular forms 1 noncommutative symmetric functions 1 partition identities 1 partition theory 1 q-series 1

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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

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

Beyond Mock Modularity: Elliptic Corrections for Higher Dyson Ranks

Claudia Alfes, Ken Ono, Ashvin Swaminathan

The paper investigates generating functions for higher Dyson ranks, revealing a hidden elliptic structure and providing explicit polynomial obstructions and correction terms that l…

math.NT2026

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

Kenny Lau, Seewoo Lee, Ken Ono

The paper develops a formalization of q‑series theory in the Lean proof assistant, building foundational structures like q‑Pochhammer symbols and Bailey's Lemma, and provides fully…

math.NT2026

Integer values of $tan (arctan 1 + arctan 2 + \dots + arctan n)$ are rare

Ken Ono

For $n \geq 1$ , we let $x_{n} := tan (k = 1 \sum n arctan k) .$ In 2008, Amdeberhan, Medina, and Moll conjectured that $x_{n} \neq \in Z$ for every $n \geq 5$ . This was kn…

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…

Algebraic geometric framework of Rogers--Ramanujan identities

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

Beyond Mock Modularity: Elliptic Corrections for Higher Dyson Ranks

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

Integer values of tan(arctan1+arctan2+⋯+arctann) are rare

Parity of k-differentials in genus zero and one

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

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

Integer values of $tan (arctan 1 + arctan 2 + \dots + arctan n)$ are rare

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