Automorphic symbols and automorphic \emph{L}-values of GL(2) over imaginary quadratic fields
Year: 2026
Type: preprint
Abstract: We study non-vanishing modulo primes of critical values of $L$-functions over imaginary quadratic fields twisted by Coates--Wiles characters. For a parallel weight two Hecke eigenform over an imaginary quadratic field, we prove that a positive proportion of Coates--Wiles characters have nonzero integral $L$-values modulo each prime in a positive-density set. The argument constructs automorphic symbols in parabolic homology with integral coefficients and expresses the critical values through their pairings with parabolic cohomology classes. A vertical family of additive averages of these pairings recovers Fourier coefficients and force the module generated by symbols to have full rank. We transfer this full-rank property to non-vanishing modulo primes. This extends the homological strategy of Kim--Sun from classical modular curves to arithmetic orbifolds, while addressing the unit obstructions specific to the imaginary quadratic setting.
Source: arXiv (Cornell University)
Author: Kwon, Jaesung
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221110634