Alladi Ramakrishnan Hall

Representation of Integers by a Family of Cubic Forms

Manoj Verma

IMSc

Under certain condition on the coefficients, we find an
asymptotic formula for the number of represenations of integers by cubic
forms which can be written as
$L_1(x_1, x_2, x_3) Q_1(x_1, x_2, x_3) + L_2(x_4, x_5, x_6) Q_2(x_4, x_5,
x_6)+ a_7 x_7^3$ where $L_1$, L_2$ are linear forms, $Q_1$, $Q_2$ are
quadratic forms and $a_7$ is a non-zero integer.