SU\G(𝔸)/K·U

ON MOD<i>p</i>REPRESENTATIONS WHICH ARE DEFINED OVER<sub><i>p</i></sub>: II

L. J. P. Kilford, Gabor Wiese

Type: Article

Publication Date: 2010-03-29

Citations: 0

DOI: https://doi.org/10.1017/s001708951000008x

Abstract

Abstract The behaviour of Hecke polynomials modulo p has been the subject of some studies. In this paper we show that if p is a prime, the set of integers N such that the Hecke polynomials T N ,χ ℓ, k for all primes ℓ, all weights k ≥ 2 and all characters χ taking values in {±1} splits completely modulo p has density 0, unconditionally for p = 2 and under the Cohen–Lenstra heuristics for p ≥ 3. The method of proof is based on the construction of suitable dihedral modular forms.

Locations

  • Glasgow Mathematical Journal - View - PDF

Similar Works

Action Title Year Authors
+ On mod p representations which are defined over F_p: II 2009 L. J. P. Kilford
Gabor Wiese
+ Modular Forms in Characteristic <i>ρ</i> 2015
+ <i>p</i>-adic families of modular forms 2021
+ Images of Pseudo-Representations and Coefficients of Modular Forms modulo p 2015 Joël Bellaïche
+ PDF Chat Computations with classical and <i>p</i>-adic modular forms 2011 Alan G. B. Lauder
+ Direct Sums of Mod<i>p</i>Characters of Gal and the Homology of<i>GL</i>(<i>n</i>, ℤ) 2013 Avner Ash
+ PDF Chat Reduction modulo <i>p</i> of cuspidal representations and weights in Serre's conjecture 2009 Michael M. Schein
+ On the Iwasawa invariants of BDP Selmer groups and BDP <i>p</i>-adic <i>L</i>-functions 2023 Antonio Lei
Katharina Müller
Jiacheng Xia
+ On Siegel modular forms of level p and their properties mod p 2010 Siegfried Böcherer
Shōyū Nagaoka
+ PDF Chat Pro-<i>p</i>-Iwahori Invariants for SL<sub>2</sub>and<i>L</i>-Packets of Hecke Modules 2015 Karol Kozioł
+ PDF Chat On mod <i>p</i> singular modular forms 2016 Siegfried Böcherer
Toshiyuki Kikuta
+ PDF Chat On <i>p</i>-adic properties of the Eichler-Selberg trace formula II 1976 Mizuho Koike
+ Vector-valued <i>p</i>-adic Siegel modular forms 2012 Takashi Ichikawa
+ On mod p properties of Siegel modular forms 2007 Siegfried Böcherer
Shōyū Nagaoka
+ PDF Chat A note on modular forms mod <i>p</i> 1983 Masao Koike
+ <i>p</i>-adic <i>L</i>-functions for GL<sub><i>n</i></sub> 2016 Debargha Banerjee
A. Raghuram
+ Prime Determinant Matrices and the Sympletic Theta Function 1984 Robert Styer
+ Modp Hecke operators and congruences between modular forms 1983 Kenneth A. Ribet
+ Kloosterman, quadratic forms and modular forms 2000 Peter Sarnak
Peter Sarnak
Kloosterman Centennial Celebration
+ Hecke's theory of modular forms and Dirichlet series : lecture notes, spring 1970 1970 Bruce C. Berndt

Works That Cite This (0)

Action Title Year Authors

Works Cited by This (19)

Action Title Year Authors
+ Handbuch der Lehre von der Verteilung der Primzahlen 1911 Edmund Landau
+ PDF Chat Dihedral Galois representations and Katz modular forms 2004 Gabor Wiese
+ The Magma Algebra System I: The User Language 1997 Wieb Bosma
John Cannon
Catherine Playoust
+ PDF Chat Factoring Hecke polynomials modulo a prime 2000 J. Brian Conrey
David W. Farmer
Peter Jake Wallace
+ PDF Chat On the irreducibility of Hecke polynomials 2008 Scott Ahlgren
+ PDF Chat On the independence of Heegner points associated to distinct quadratic imaginary fields 2007 Michael Rosen
Joseph H. Silverman
+ On mod p modular representations which are defined over \F_p 2006 L. J. P. Kilford
+ PDF Chat Irreducibility of Hecke polynomials 2003 Srinath Baba
M. Ram Murty
+ On the Eigenvalues of the Hecke OperatorT2 1996 Kevin Buzzard
+ PDF Chat On the exponent of the ideal class groups of complex quadratic fields. 1972 David W. Boyd
Hershy Kisilevsky