Factoring Hecke polynomials modulo a prime
J. Brian Conrey, David W. Farmer, Peter Jake Wallace
Abstract
Let TN,chip,k(x) be the characteristic polynomial of the Hecke operator Tp acting on the space of cusp forms Sk(N,chi). We describe the factorization of TN,chip,k(x) mod l as k varies, and we explicitly calculate those factorizations for N=1 and small l. These factorizations are used to deduce the irreducibility of certain T1,1q,k(x) from the irreducibility of T1,12,k(x).
Create a lesson
Related papers
Value distribution of multiplicative functions along linear fractional sequences
Sun-Kai Leung
Delta theory of Anderson Modules II: Hodge-Pink structure
Sudip Pandit, Arnab Saha
Integers divisible by a shifted prime in a given interval
Rebecca Abi Abdallah, Valeriya Kovaleva, Jeremy Schlitt et al.
On Piatetski-Shapiro primes from almost primes
Yuhua Zhao, Jinjiang Li, Linji Long et al.
On Consecutive Non-primitive Elements over Finite Fields
Bidushi Sharma, Dhiren Kumar Basnet
Birch's theorem over function fields with quadratically many variables
Matthew Hase-Liu