Increasing the p-Selmer rank by twisting

In this paper, we study the $p$-Selmer groups in the family of $p$-twists of an elliptic curve $E$ over a number field $K$. We prove that if $E\mathrm{/}K$ is an elliptic curve over a number field $K$, and if $d$ is congruent to the dimension of the Selmer group of $E\mathrm{/}K$ modulo $2$ and is greater than that dimension, then there exist infinitely many characters $\chi \in \text{Hom}(G_K,{\mu }_p)$ such that ${\text{dim}}_{{\mathbb{F}}_p}({\text{Sel}}_p(E\mathrm{/}K,\chi ))=d$ under certain conditions.