On the representation of numbers by quaternary and quinary cubic forms: I

C. Hooley. "On the representation of numbers by quaternary and quinary cubic forms: I." Acta Arithmetica 173.1 (2016): 19-39. <http://eudml.org/doc/278997>.

@article{C2016,
abstract = {On the assumption of a Riemann hypothesis for certain Hasse-Weil L-functions, it is shewn that a quaternary cubic form f(x) with rational integral coefficients and non-vanishing discriminant represents through integral vectors x almost all integers N having the (necessary) property that the equation f(x)=N is soluble in every p-adic field ℚₚ. The corresponding proposition for quinary forms is established unconditionally.},
author = {C. Hooley},
journal = {Acta Arithmetica},
keywords = {quaternary cubic forms; quinary cubic forms},
language = {eng},
number = {1},
pages = {19-39},
title = {On the representation of numbers by quaternary and quinary cubic forms: I},
url = {http://eudml.org/doc/278997},
volume = {173},
year = {2016},
}

TY - JOUR
AU - C. Hooley
TI - On the representation of numbers by quaternary and quinary cubic forms: I
JO - Acta Arithmetica
PY - 2016
VL - 173
IS - 1
SP - 19
EP - 39
AB - On the assumption of a Riemann hypothesis for certain Hasse-Weil L-functions, it is shewn that a quaternary cubic form f(x) with rational integral coefficients and non-vanishing discriminant represents through integral vectors x almost all integers N having the (necessary) property that the equation f(x)=N is soluble in every p-adic field ℚₚ. The corresponding proposition for quinary forms is established unconditionally.
LA - eng
KW - quaternary cubic forms; quinary cubic forms
UR - http://eudml.org/doc/278997
ER -