2026/08/01 by Subham Roy, Pavlo Yatsyna
Mathematics · #math.NT #msc:11R06 #msc:11P32 #msc:11C08
27 pages; comments are welcome!
arxiv created 2026/08/01 · arxiv updated 2026/08/04
We show that the minimal degree of a Salem number with prescribed negative trace is bounded below by T2/log T and above by T2log T, up to explicit constants and lower-order terms, where T is the absolute value of the trace. This improves the previous doubly exponential upper bound of McKee and Smyth. Building on their construction, we also prove that for every prescribed negative trace there exists a constant d0 such that Salem numbers of that trace exist in every even degree exceeding d0.