Geodesic
Lower estimates of sums of polynomial characters
Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 67-72

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An infinite sequence of primes $p$ is formulated, and for each $p$ polynomials of form $ax^n+b$, $(a,p=(b,p)=1$, are indicated such that $$\sum_{x=1}^p\biggl(\frac{ax^n+b}p\biggr),\quad n\asymp\frac p{\log p}.$$ 
@article{MZM_1973_14_1_a8,
     author = {A. A. Karatsuba},
     title = {Lower estimates of sums of polynomial characters},
     journal = {Matemati\v{c}eskie zametki},
     pages = {67--72},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a8/}
}
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A. A. Karatsuba. Lower estimates of sums of polynomial characters. Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 67-72. http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a8/