3 papers
math.CO2026
Remarks on the disproof of the unit distance conjecture
Noga Alon, Thomas F. Bloom, W. T. Gowers +6
We present a short, digested, human-verified version of the recent OpenAI-generated counterexample to the ErdÅs unit distance conjecture, and a sequence of reflections on it. The…
math.NT2025
Secondary terms in the counting functions of quartic fields
Arul Shankar, Jacob Tsimerman
We prove that the smoothed counting function of the set of quartic fields, satisfying any finite set of local conditions, can be written as a linear combination of $X,X^{5/6}\log X…
math.NT2025
Secondary terms in the counting functions of quartic fields II
Arul Shankar, Jacob Tsimerman
We determine the smoothed counts of -quartic fields with bounded discriminant, satisfying any finite specified set of local conditions, as the sum of two main terms with a pow…