Newton polygons of $L$-functions of polynomials $x^d+a{x}^{d-1}$ with $p\equiv -1\mathrm{mod}d$

Yi Ouyang, Shenxing Zhang

For prime $p\equiv -1\mathrm{mod}d$ and $q$ a power of $p$, we obtain the slopes of the $q$-adic Newton polygons of $L$-functions of $x^d+a{x}^{d-1}\in {\mathbb{F}}_q[x]$ with respect to fini…