Polya-Vinogradov for GL(n, F_p)

Date(s) : 22/06/2017   iCal
14 h 00 min - 15 h 00 min

We prove an analogue of the Polya-Vinogradov inequality for character sums where, instead of characters of the group GL(1, F_p) of invertible elements in F_p, we work with representations of the group GL(n, F_p) for n >1. As an application, in analogy with the question of the least quadratic non-residue, we obtain a bound for the size of the integer matrix of smallest size which is not congruent to a square matrix modulo p. Here, p is a prime and by size of a real matrix, we mean the maximum of its entries.


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