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Article Citation - WoS: 1Citation - Scopus: 1The Number of Irreducible Polynomials Over Finite Fields With Vanishing Trace and Reciprocal Trace(Springer, 2022) Cakiroglu, Yagmur; Yayla, Oguz; Yilmaz, Emrah SercanWe present the formula for the number of monic irreducible polynomials of degree n over the finite field F-q where the coefficients of x(n)(-1) and x vanish for n >= 3. In particular, we give a relation between rational points of algebraic curves over finite fields and the number of elements a is an element of F-qn for which Trace(a) = 0 and Trace(a(-1)) = 0.Article Citation - WoS: 2Citation - Scopus: 2Further Results on Fibre Products of Kummer Covers and Curves With Many Points Over Finite Fields(Amer inst Mathematical Sciences-aims, 2016) Ozbudak, Ferruh; Temur, Burcu Gulmez; Yayla, OguzWe study fibre products of an arbitrary number of Kummer covers of the projective line over F-q under suitable weak assumptions. If q - 1 = r(n) for some prime r, then we completely determine the number of rational points over a rational point of the projective line. Using this result we obtain explicit examples of fibre products of three Kummer covers supplying new entries for the current table of curves with many points (http://www.manypoints.org,October 31 2015).
