11 citations · 25 across the 21 of their papers we have counts for
22 papers
Positive quasimodular forms and the sign uncertainty principle
Seewoo Lee
For every positive integer divisible by , we prove the following new upper bound for the Bourgain-Clozel-Kahane sign uncertainty constant: \[ \mathrm{A}_+(d) \le \sqrt{2 \le…
Formalized -series: The Rogers-Ramanujan Identities and Beyond
Kenny Lau, Seewoo Lee, Ken Ono
The theory of -series and basic hypergeometric series plays a crucial role at the intersection of combinatorics, number theory, and representation theory. From the classical par…
Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves
Barinder S. Banwait, Xiaoyu Huang, Kyu-Hwan Lee +3
We investigate the extent to which the coefficients of the reduced minimal Weierstrass model of an elliptic curve are determined by the Diric…
Progress in Formalizing Sphere Packing in Dimension 8
Sidharth Hariharan, Christopher Birkbeck, Seewoo Lee +4
In 2016, Viazovska famously solved the sphere packing problem in dimension , using modular forms to construct a 'magic' function satisfying optimality conditions determined by C…
Lean-GAP: A Dataset of Formalized Graduate Algebra Problems
Seewoo Lee, Byung-Hak Hwang, Hyojae Lim +10
We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pi…
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…
Ties in Function Field Prime Races
Graeme Bates, Ryan Jesubalan, Seewoo Lee +2
The function field analogue of Chebyshev's bias was first studied by Cha. In this paper, we study *ties* in this race, namely collections of distinct congruence classes $c_1, \dots…
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 such that, in base , every one-digit extension is non-square-free. In base , the stochastic…
Almost all primes are partially regular
Evan Chen, Chris Cummins, Ben Eltschig +18
For odd primes , we let be the th cyclotomic field and let denote its Teichmuller character. For , we say that an odd prime is partially…
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_…
Powerful Fibonacci polynomials over finite fields
Graeme Bates, Ryan Jesubalan, Seewoo Lee +2
Bugeaud, Mignotte, and Siksek proved that the only perfect powers in Fibonacci sequence are 0, 1, 8, and 144. In this paper, we study the polynomial analogue of the problem. Especi…
Modulation groups
Jayce R. Getz, Armando Gutiérrez Terradillos, Farid Hosseinijafari +6
Conjectures of Braverman and Kazhdan, Ngô and Sakellaridis have motivated the development of Schwartz spaces for certain spherical varieties. We prove that under suitable assumptio…
Shanks' bias in function fields
Seewoo Lee
We study the function field analogue of Shanks bias. For Liouville function , we compare the number of monic polynomials with and for…
Machines Learn Number Fields, But How? The Case of Galois Groups
Kyu-Hwan Lee, Seewoo Lee
By applying interpretable machine learning methods such as decision trees, we study how simple models can classify the Galois groups of Galois extensions over of degre…
Formalizing Mason-Stothers Theorem and its Corollaries in Lean 4
Jineon Baek, Seewoo Lee
The ABC conjecture implies many conjectures and theorems in number theory, including the celebrated Fermat's Last Theorem. Mason-Stothers Theorem is a function field analogue of th…
Algebraic proof of modular form inequalities for optimal sphere packings
Seewoo Lee
We give algebraic proofs of Viazovska and Cohn-Kumar-Miller-Radchenko-Viazovska's modular form inequalities for 8 and 24-dimensional optimal sphere packings.
HETAL: Efficient Privacy-preserving Transfer Learning with Homomorphic Encryption
Seewoo Lee, Garam Lee, Jung Woo Kim +2
Transfer learning is a de facto standard method for efficiently training machine learning models for data-scarce problems by adding and fine-tuning new classification layers to a m…
unit equilateral triangles cannot cover an equilateral triangle of side if all triangles have parallel sides
Jineon Baek, Seewoo Lee
Conway and Soifer showed that an equilateral triangle of side with sufficiently small can be covered by unit equilateral triangles…
Non-archimedean Sendov's Conjecture
Daebeom Choi, Seewoo Lee
We prove non-archimedean analogue of Sendov's conjecure. We also provide complete list of polynomials over an algebraically closed non-archimedean field that satisfy the optima…
Assessment Modeling: Fundamental Pre-training Tasks for Interactive Educational Systems
Youngduck Choi, Youngnam Lee, Junghyun Cho +9
Like many other domains in Artificial Intelligence (AI), there are specific tasks in the field of AI in Education (AIEd) for which labels are scarce and expensive, such as predicti…
Quantum modular forms and Hecke operators
Seewoo Lee
It is known that there is an one-to-one correspondence among the space of cusp forms, the space of homogeneous period polynomials and the space of Dedekind symbols with polynomial…
Toy Teichmüller spaces of real dimension 2: the pentagon and the punctured triangle
Yudong Chen, Roman Chernov, Marco Flores +3
We study two -dimensional Teichmüller spaces of surfaces with boundary and marked points, namely, the pentagon and the punctured triangle. We show that their geometry is quite d…