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We show that there exists a connection between two types of objects: somekind of resultantal varieties over C, from one side, and varieties of twists ofthe tensor powers of the Carlitz module such that the order of 0 of itsL-functions at infinity is a constant, from another side. Obtained results areonly a starting point of a general theory. We can expect that it will bepossible to prove that the order of 0 of these L-functions at 1 (i.e. theanalytic rank of a twist) is not bounded --- this is the function field caseanalog of the famous conjecture on non-boundedness of rank of twists of anelliptic curve over Q. The paper contains a calculation of a non-trivialpolynomial determinant.

Resultantal varieties related to zeroes of L-functions of Carlitz modules