2012/05/13 by Alexandr N. Grishkov, Grishkov, Alexandr N., Dmitry Logachev +1 · 1 citation
Computer Science · Mathematics · #05A19 #11G09 #13C40 #13P15 #14M10 #14M12 #14Q15 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1205.2900
openalex publication_date 2012/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that there exists a connection between two types of objects: some\nkind of resultantal varieties over C, from one side, and varieties of twists of\nthe tensor powers of the Carlitz module such that the order of 0 of its\nL-functions at infinity is a constant, from another side. Obtained results are\nonly a starting point of a general theory. We can expect that it will be\npossible to prove that the order of 0 of these L-functions at 1 (i.e. the\nanalytic rank of a twist) is not bounded --- this is the function field case\nanalog of the famous conjecture on non-boundedness of rank of twists of an\nelliptic curve over Q. The paper contains a calculation of a non-trivial\npolynomial determinant.\n