Stevens, GlennBusuioc, Cecilia2024-05-222024-05-222023-11-27G. Stevens, C. Busuioc. "Modular Symbols with values in Beilinson-Kato Distributions" Transactions of the American Mathematical Society.0002-9947https://hdl.handle.net/2144/48825For each integer n≥1, we construct a GLn(ℚ)-invariant modular symbol 𝜉_n with coefficients in a space of distributions that takes values in the Milnor K_n-group of the modular function field. The Siegel distribution μ on ℚ2, with values in the modular function field, serves as the building block for 𝜉_n; we define 𝜉_n essentially by taking the n-Steinberg product of μ. The most non-trivial part of this construction is the cocycle property of 𝜉_n; we prove it by using an induction on n based on the first two cases 𝜉_1 and 𝜉_2; the first case is trivial, and the second case essentially follows from the fact that Beilinson-Kato elements in the Milnor K_2-group modulo torsion satisfy the Manin relations.Pure mathematicsApplied mathematicsGeneral mathematicsArticle2024-02-2510.48550/arXiv.2311.14620907264