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Existence problems of primitive polynomials over finite fields

Presern, MatejaUniversity of Glasgow2007

… case developing methods involving the use of character sums and sieving techniques. When the characteristic of the field is 2 or 3, we also use p-adic analysis. In addition to proving the previously unestablished cases of the conjecture, we also offer shorter and self-contained proof of the …

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Explicit multiplicative relations between Gauss sums

Murray, Brian J.Mathematics2022

… that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product …

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On congruence function fields with many rational places

Mak, Kit HoUniversity of Illinois at Urbana-Champaign2012

… relies heavily on various estimates of twisted character sums over function fields.

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The correction factor in Artin type problems

Fakhari, Milad, University of Lethbridge. Faculty of Arts and Science2021

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