Oscillation patterns in L-functions of Dirichlet characters
A Dirichlet character χ mod q is a completely multiplicative function from integers to complex numbers with period q. The character values χ(p) for primes play a role analogous to aₚ for elliptic curves.
Following the elliptic curve discovery, mathematicians proved that murmuration-like oscillations appear in averaged character sums. The patterns depend on whether the character is even or odd.
This universality across different number-theoretic objects suggests murmurations are a fundamental phenomenon related to the analytic properties of L-functions and the distribution of primes.