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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+…
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…
math.NT2026★ 2 cited
A catalog of interesting and useful Lambert series identities
Maxie Dion Schmidt
A Lambert series generating function is a special series summed over an arithmetic function defined by \[ L_f(q) := \sum_{n \geq 1} \frac{f(n) q^n}{1-q^n} = \sum_{m \geq 1} (f…