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Comp."],"abstract":"<p>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 bound to 1.80203. Our method adds new constraints to Smyth\u2019s linear programming method to decrease the number of variables required in the new problem of interest. This allows for faster convergence recovering Schur\u2019s bound in the simplest case and Siegel\u2019s bound in the second simplest case of our new family of bounds. We also prove the existence of a unique optimal solution to our newly phrased problem and express the optimal solution in terms of polynomials. Lastly, we solve this new problem numerically with a gradient descent algorithm to attain the new bound 1.80203.<\/p>","DOI":"10.1090\/mcom\/4004","type":"journal-article","created":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T09:23:16Z","timestamp":1722936196000},"page":"2005-2040","source":"Crossref","is-referenced-by-count":0,"title":["New lower bounds for the Schur-Siegel-Smyth trace problem"],"prefix":"10.1090","volume":"94","author":[{"given":"Bryce","family":"Orloski","sequence":"first","affiliation":[]},{"given":"Naser","family":"Talebizadeh Sardari","sequence":"additional","affiliation":[]},{"given":"Alexander","family":"Smith","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2024,8,6]]},"reference":[{"issue":"253","key":"1","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1090\/S0025-5718-05-01776-X","article-title":"The trace of totally positive algebraic integers","volume":"75","author":"Aguirre, Juli\u00e1n","year":"2006","journal-title":"Math. 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