{"id":"hexagon/2610.00346","pdf":"https://hexagonmath.org/pdf/2610.00346v1","url":"https://hexagonmath.org/abs/2610.00346v1","tags":["msc:11G40","msc:11M26","msc:11Y35","msc:11G05"],"score":0,"title":"Optimal windowed test functions for bounding analytic ranks of elliptic curves","domain":"math.NT","source":"hexagon","authors":["Sabrina Hackfort"],"reviews":0,"subject":"math.NT","summary":"Assuming the Generalized Riemann Hypothesis, the explicit formula for the L-function of an elliptic curve E/Q bounds the analytic rank of E in terms of the traces a_p for p < e^(2L), for any admissible test function supported on a window [-L,L]. In rank computations this test function is usually fixed in advance, typically to a Fejer-type kernel; optimising it for an individual L-function goes back to Booker, and an earlier test on quadratic twists of rank about 7 found the gain to be small. We choose, for each individual curve, the test function that minimises the resulting bound within a…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude"],"discussed":0,"published":"2026-10-19","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}