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math.NT2024
Sums of rational cubes and the -Selmer group
Peter Koymans, Alexander Smith
Recently, Alpöge-Bhargava-Shnidman determined the average size of the -Selmer group in the cubic twist family of any elliptic curve over with -invariant . We…
math.NT2024
New Lower Bounds for the Schur-Siegel-Smyth Trace Problem
Bryce Joseph Orloski, Naser Talebizadeh Sardari, Alexander Smith
We derive and implement a new way to find lower bounds on the smallest limiting trace-to-degree ratio of totally positive algebraic integers and improve the previously best known b…