Number Theory
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Paper The quasi-Riemann hypothesis
Proves that every Dirichlet L-function, including \zeta(s), is zero-free in \Re s\gt 7/8, resolving the quasi-Riemann hypothesis. The same half-plane is zero-free for every finite-order Hecke L-function over…
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Paper Uniformly bounded components of Gaussian-prime graphs
Proves the Gaussian moat conjecture: no infinite walk through distinct Gaussian primes can have uniformly bounded steps. More strongly, for every distance bound D, the graph joining Gaussian primes at distance at most D…
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Paper A quadratic bound for Jacobsthal’s function
Answers Jacobsthal's quadratic-bound question: every interval of Ck^2 consecutive integers contains an integer coprime to any prescribed positive integer with at most k distinct prime divisors, for an absolute…
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Paper Short Egyptian fractions
Every rational a/b with 1\le a\lt b is a sum of O(\log\log b) distinct positive unit fractions. The worst-case minimum number of terms has the same order, resolving Erdős’s conjecture on short Egyptian…
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Paper Potential integral density on curve character varieties
Resolves the determinant-one curve case of Litt's integral-density question. For every smooth connected complex algebraic curve and every rank, integral points become Zariski dense in every component of its SLr…
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Paper Squarefree quartics and power-free polynomial values
Proves the squarefree-values conjecture for irreducible integer quartics with no fixed prime-square divisor: squarefree values on positive integers have the predicted positive Euler-product density. More generally,…
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Paper The Deligne–Drinfeld conjecture
Proves that the rational Grothendieck–Teichmüller Lie algebra, with the Ihara bracket, is freely generated by one element in each odd weight 3, 5, 7, …, resolving the Deligne–Drinfeld conjecture. () Manuscript September…
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