Evan Chen

collaborators

11 papers

math.CO2026

Record compositions of alternating permutations and noncommutative symmetric functions

Evan Chen, Ken Ono, Michal Mogielnicki

Amdeberhan, Shareshian, and Stanley recently proved that a function $φ$ arising in the theory of partition Eisenstein series counts the alternating permutations of ${1, \dots, 2 n}$ …

math.NT2026

Thakur's hypotheses on power sums of $F_{q} [t]$

Evan Chen, Ken Ono

In his 2009 paper, Thakur posed three conjectural hypotheses for the degrees of the power sums \[ S_d(k)=\sum_{\substack{a\in \mathbb F_q[t] \text{ monic}\\ °a=d}} a^{-k} \qquad\te…

math.NT2026

Four-digit Kaprekar dynamics in odd bases

Evan Chen, Ken Ono, Richard E. Schwartz +1

Start with four digits, arrange them in both descending and ascending order, subtract, and repeat. This simple process is known as the Kaprekar routine, famous in base ten for send…

math.CO2026

Reciprocals of Partition Polynomials

Evan Chen, Ken Ono, Jujian Zhang

Ballantine--Beck--Feigon--Maurischat introduced the subsum polynomial \[ \operatorname{sp}(λ,x):=\prod_i (1+x^{λ_i}) \] attached to an integer partition $λ$ , and studied rational f…

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.DS2026

On the paucity of lattice triangles

David Kurniadi Angdinata, Evan Chen, Ken Ono +3

A rational triangle $T$ (one whose angles are rational multiples of $π$ ) unfolds to a translation surface $X_{T}$ . The lattice triangle problem asks to classify those $T$ for which…

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_…

math.NT2025

Semi-Lie arithmetic fundamental lemma for the full spherical Hecke algebra

Evan Chen

As an analog to the Jacquet-Rallis fundamental lemma that appears in the relative trace formula approach to the Gan-Gross-Prasad conjectures, the arithmetic fundamental lemma was p…

Record compositions of alternating permutations and noncommutative symmetric functions

Thakur's hypotheses on power sums of Fq​[t]

Four-digit Kaprekar dynamics in odd bases

Reciprocals of Partition Polynomials

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

On the paucity of lattice triangles

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

Semi-Lie arithmetic fundamental lemma for the full spherical Hecke algebra

Thakur's hypotheses on power sums of $F_{q} [t]$

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