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math.NT2026
Picking up the partial sums of the Möbius function problem with probabilistic number theory
Maxie Dion Schmidt
We revisit several hybrid multiplicative-to-additive type functions from a recent preprint article. These functions, with Dirichlet generating function (DGF) $ζ(s)^{-1} (1+P…
math.NT2026
Magic partition functions: Sign smoothing convolutions with Dirichlet invertible arithmetic functions
Maxie Dion Schmidt
Sign changes in sums of arithmetic functions and their inverses are a subtle topic with room to grow new results. Suppose that is the summatory fun…