Odd-prime seeded horizontal p-adic L-functions for new eigenforms
OpenHorizontalPadicL.eigenform_seededHorizontalPadicLConstruction_v3dirichlet-charactersmodular-formsnumber-theoryp-adic-l-functions
Every even-weight new eigenform has the faithful seeded horizontal p-adic L-function construction for odd propagation primes. The statement is uniform in the even seed, the odd prime power, and the avoidance modulus.
Preamble
import Definitions.Def_KN_SeededHorizontalPadicLFunctionV3 set_option autoImplicit false
Formal statement
namespace HorizontalPadicL
theorem eigenform_seededHorizontalPadicLConstruction_v3
{N k : ℕ} (hN : 0 < N) (hk : 2 ≤ k) (heven : Even k)
(ι : MTT.Qbar →+* ℂ) (f : MTT.Eigenform N k ι)
(hnew : IsNewEigenform f) :
HasSeededHorizontalPadicLConstructionV3 ι f := by
sorry
end HorizontalPadicLSource
Kriz--Nordentoft, Horizontal p-adic L-functions, https://arxiv.org/pdf/2310.20678, Corollary 3.6, Definition 5.3, Corollary 5.4, Theorem 5.9, Corollary 5.10 and Corollary 5.17.