7 papers · 1 filter
The 196560 auxiliary-function conjecture for the Leech lattice
Yutong Zhang, Yaoran Yang
Cohn and Kumar conjectured in 2009 that there is a radial Schwartz function satisfying for , for , $g(2)…
A Proof of a Conjecture of Zhi-Wei Sun on a Truncated Legendre-Symbol Determinant
Yaoran Yang, Gaishi Yang, Yutong Zhang
We prove Conjecture~3.4 of Zhi-Wei Sun by evaluating, for every prime , a truncated Legendre-symbol determinant as . The argument reduce…
A Uniform Random-Lattice Tail Bound for the SVP Kissing-Profile Parameter
Yutong Zhang, Yaoran Yang
A recent SICOMP paper on classical and quantum algorithms for the shortest vector problem introduced a lattice-dependent parameter \(γ(L)\), bounded universally in the exponential…
A Local Valuation Criterion for Quadratic-Permutation Interleaved Zadoff--Chu Sequences
Yutong Zhang, Yaoran Yang
Berggren and PopoviÄ introduced quadratic-permutation-polynomial interleaved Zadoff--Chu sequences and, from exhaustive data, conjectured that all normalized QPP-interleaved Zadof…
Two determinant evaluations in Sun's conjectures involving Legendre symbols
Yaoran Yang, Yutong Zhang
We prove two determinant evaluations attached to Sun's conjectures on matrices of Legendre symbols. The first one resolves the \(p\equiv1\pmod4\) part of Conjecture 4.8(i) by reduc…
Sun-type determinant and permanent congruences
Yaoran Yang, Yutong Zhang
Sun proposed a list of congruence and quadratic-residue conjectures for determinants and permanents over residue classes modulo a prime. This article gives a uniform treatment of C…