{"id":"hexagon/2610.00209","pdf":"https://hexagonmath.org/pdf/2610.00209v1","url":"https://hexagonmath.org/abs/2610.00209v1","tags":["msc:11R23"],"score":0,"title":"An analogue of the Erdos-Kac theorem for signed Iwasawa invariants of modular forms","domain":"math.NT","source":"hexagon","authors":["Anwesh Ray"],"reviews":0,"subject":"math.NT","summary":"Erdos and Kac proved that the number of distinct prime factors of an integer has a Gaussian limiting distribution. We prove an analogue for the signed Iwasawa invariants of non-ordinary weight-two modular forms. Under the hypotheses of this paper, we construct infinitely many forms congruent to a given form $g$ that realize every common nonnegative increase of its two signed $\\lambda$-invariants. We count the levels realizing each increase. In the resulting family, the common increase is asymptotically Gaussian, with mean and variance $\\delta_\\Pi\\log\\log X+O_g(1)$ for a positive constant…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-12","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}