What is...the Cantor sequence? 

Classically, Gauss genus theory of quadratic forms for quadratic fields Q(-d^1/2) is derived from the general linear group GL(2, Z). The action the group SL(2, Z) on the upper half plane H is the starting point of modular functions and modular forms. See “Primes of the form x^2 + ny^2” (1989) which includes an account of the genus theory found in Gauss’s Disquisitiones Arithmeticae. Representations of both modular forms and quadratic fields can be equated by Serre’s modularity conjecture proven by Khare and Wintenberger. This logarithmic asymptotic staircase looks similar to the psi function ψ(x) = x - log(2π) + {zeros of ζ} determined by zeros of Riemann zeta function bounded by the prime number theorem. I wonder if the Cantor set may describe a similar psi function determined by the zeros of the L-functions of modular forms and their equivalent quadratic fields. The Cantor function and Riemann zeta function both described by Bernoulli numbers. Note "Integrals Related to the Cantor Function." (2004) by Gorin, E. A. and Kukushkin, B. N. The Cantor function is a map between the interval c: I -> I to itself with a ternary function of deleting the center 1/3. Following A^1-homotopy theory this the interval can be replaced by the affine line A^1. This equivalence is a result of the Thom-Pontryagin theorem between the algebraic cobordism groups A of a smooth quasi-projective scheme over field k (ie affine variety A^n_k such as affine line A^1_k) and some homotopy groups π_A given by classical homotopy. A commutative diagram can be constructed to compose both from the equivalence class of homotopy groups from the homotopic paths of the interval f: I -> X and the equivalence class of algebraic paths of the affine line g: A^1 -> Y. There is a quadratic integer ring Z[ω] = {a + ωb} where ω = (1 + D^1/2)/2 with discrimination D of associated to an quadratic field Q(D^1/2). The coordinate ring is equivalent to the affine line Z[ω] = A^1 by Hilbert’s Nullstellensatz. The automorphism a: A^1 -> A^1 described by the Cantor map descends to the ring of integers a quadratic integers. Quadratic integers form lattices which can be considered equivalent and furthermore automorphic up to homothety given by matrices in SL(2,Z).

very unexpected!