Trinity College London

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20062026

most citedA Chirality-Based Quantum Leap

216 citations

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math.NT2026

Erdős Problem 684 at Density One: Small-prime Parts of Binomial Coefficients and Gaussian Fluctuations

Eric Li

For $0 \leq k \leq n$ , let $u (n, k)$ be the largest divisor of $(k n)$ whose prime factors are at most $k$ . Erdős Problem #684 concerns the special threshold $u (n, k) > n^{2}$ and asks…

math.NT2020★ 3 cited

Extremal problems for GCDs

Ben Green, Aled Walker

We prove that if $A \subseteq [X, 2 X]$ and $B \subseteq [Y, 2 Y]$ are sets of integers such that $g cd (a, b) \geq D$ for at least $δ ∣ A ∣∣ B ∣$ pairs $(a, b) \in A \times B$ then $|A||B|…

math.NT2014★ 6 cited

Algebraic functional equations and completely faithful Selmer groups

Tibor Backhausz, Gergely Zábrádi

Let $E$ be an elliptic curve---defined over a number field $K$ ---without complex multiplication and with good ordinary reduction at all the primes above a rational prime $p \geq 5$ …

math.NT2008★ 6 cited

Proof of the Main Conjecture of Noncommutative Iwasawa Theory for Totally Real Number Fields in Certain Cases

Mahesh Kakde

Fix an odd prime $p$ . Let $G$ be a compact $p$ -adic Lie group containing a closed, normal, pro- $p$ subgroup $H$ which is abelian and such that $G / H$ is isomorphic to the additive g…