From the 1 of 8 linked papers with an AI index.
8 papers
Algebraic geometric framework of Rogers--Ramanujan identities
Yifeng Huang, Kenny Lau, Ken Ono +1
The Rogers--Ramanujan identities equate a -series whose exponents are governed by a quadratic form with an infinite product supported on two residue classes modulo~. Identiti…
Modularity of Point Counts for the Curves : New Rogers--Ramanujan Identities
Kenny Lau, Ken Ono
For coprime , let be the set of commuting pairs of nilpotent matrices over with . Huang, Jiang, and Oblomkov as…
Formalized -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…
Parity of -differentials in genus zero and one
Dawei Chen, Evan Chen, Kenny Lau +2
Here we completely determine the spin parity of -differentials with prescribed zero and pole orders on Riemann surfaces of genus zero and one. This result was previously obtaine…
Fel's Conjecture on Syzygies of Numerical Semigroups
Evan Chen, Chris Cummins, GSM +18
Let be a numerical semigroup and its semigroup ring. The Hilbert numerator of determines normalized alternating syzygy power sums $K_…
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…