# On a Problem of Mordell with Primitive Roots

@inproceedings{Cobeli2009OnAP, title={On a Problem of Mordell with Primitive Roots}, author={Cristian Cobeli}, year={2009} }

We consider the sums of the form $$ S=\sum_{x=1}^{N} \exp\big((ax+b_1g_1^x+... +b_rg_r^x)/p \big) $$, where $p$ is prime and $g_1,..., g_r$ are primitive roots $\pmod p$. An almost forty years old problem of L. J. Mordell asks to find a nontrivial estimate of $S$ when at least two of the coefficients $b_1,...,b_r$ are not divizible by $p$. Here we obtain a nontrivial bound of the average of these sums when $g_1$ runs over all primitive roots $\pmod p$.

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