For a certain class of functions ƒ: Z ⟶ C an upper bound is obtained for the sum Σa+H n=a+1f(n). This bound is used to give a proof of a classical inequality due to Pólya and Vinogradov that does not require the value of the modulus of the Gauss sum and to obtain an estimate of the sum of Legendre symbols ΣH x=1((Rgx + S)/P), where g is a primitive root of the odd prime p, 1≤ H≤ p− 1 and RS is not divisible by p.

Additional Metadata
Keywords Character sum, Inequality, Pólya-Vinogradov inequality
Persistent URL dx.doi.org/10.1090/S0002-9939-1992-1068118-6
Journal Proceedings of the American Mathematical Society
Citation
Dobrowolskj, E. (Edward), & Williams, K.S. (1992). An upper bound for the sum Σa+H n=a+1f(n) for a certain class of functions ƒ. Proceedings of the American Mathematical Society, 114(1), 29–35. doi:10.1090/S0002-9939-1992-1068118-6