Onp-Adic Zeros of Additive Forms of Even Degree Original Research Article

In this paper it is proved that the pairf=a1xk1+…+anxkn,g=b1xk1+…+bnxkn, withk=pτ(p−1)k0and (k0, p)=1, has a commonp-adic zero providedngreater-or-equal, slanted2k2+w(p, τ), wherew(p, τ)=1/(log p+(1/τ) log(p−1)). It is also proved that ifngreater-or-equal, slanted2k2, then the pairf, ghas a commonp-adic zero provided thatk0greater-or-equal, slanted2τ.