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Extreme Values of Euler-Kronecker Constants

   | 30 oct 2021

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In a family of Sn-fields (n ≤ 5), we show that except for a density zero set, the lower and upper bounds of the Euler-Kronecker constants are (n − 1) log log dK+ O(log log log dK) and loglog dK + O(log log log dK), resp., where dK is the absolute value of the discriminant of a number field K.