Author

David Niedbala Giraudin

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Preprint Oct 2026

The proportion of polynomials over F_2 with positive orthogonal multiplicity

Let A = F_2[T]. The orthogonal multiplicity m(f) of a monic f in A of degree d>= 1 is the number of g in A with deg g<d, gcd(g,f) = 1, and all partial quotients of g/f of degree one. Blackburn (1998) asked how the proportion p(d) of monic polynomials of degree d with m(f)>0 behaves as d tends to infinity. We attach to...

David Niedbala Giraudin · 0 citations

Review Sep 2026

An explicit family of twists of the Carlitz module with unbounded analytic rank

Grishkov and Logachev have asked (Problem 1.4 of their recent survey) whether, for a fixed finite field F_q, the analytic ranks of the twists of the Carlitz module are bounded. We answer this in the negative for every q>= 3. For q = p^s and n>= 1 put P_{q,n} = (theta^(q^n) - theta)^(q-2). We show that the directed grap...

David Niedbala Giraudin · 0 citations