collaborators

9 papers

math.NT2026

A new upper bound for the irrationality exponent of

David Niedbala Giraudin

We prove that the irrationality exponent of satisfies . The best published bound is 5.095412 (Zudilin, 2014); a bound 5.0495243 with a machine-check…

math.NT2026

The proportion of polynomials over F_2 with positive orthogonal multiplicity

David Niedbala Giraudin

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…

math.NT2026

New bounds for the integer Chebyshev constant of [0,1]

David Niedbala Giraudin

The integer Chebyshev constant of [0,1] has been bracketed by 0.4213 <= t_Z([0,1]) <= 0.422685 since the work of Pritsker (2005) and of Flammang (2014). We prove 0.4222286000 <= t_…

math.NT2026

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

David Niedbala Giraudin

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…

math.NT2026

A closed-form law for the Salikhov-Zeilberger-Zudilin-Bai family, and computational evidence that Bai's point is optimal

David Niedbala Giraudin

Salikhov (2008), Zeilberger-Zudilin (2020) and Bai (2026) bound the irrationality measure of pi with the same shape of complex integral. This note gives one closed-form law mu(a0,a…

math.NT2026

An infinite family of counterexamples to Goss's conjecture on L-functions of cyclotomic function fields

David Niedbala Giraudin

Let p be a prime, q = p, A = F_p[T], and let P be a monic irreducible of degree d with cyclotomic function field K_P and mod-P Teichmuller character omega_P. For a character chi =…

math.NT2026

A new lower bound for the Schur-Siegel-Smyth trace problem

David Niedbala Giraudin

We prove that lambda_SSS >= 1.80220 for the smallest limiting trace-to-degree ratio of totally positive algebraic integers, improving the bound 1.80203 obtained by Orloski, Talebiz…

math.NT2026

A new upper bound for the irrationality exponent of zeta(3)

David Niedbala Giraudin

We prove that the irrationality exponent of satisfies , improving the bound obtained by Rhin and Viola in 2001, which has been the best known…

math.NT2026

A counterexample to a conjecture of Thakur on Carlitz-Wieferich primes

David Niedbala Giraudin

Let A = F_q[T] with q a power of an odd prime p, let [n] = T^(q^n) - T, and let rho be the Carlitz module. A monic prime P of A is a c-Wieferich prime (to base 1) if rho_P(1) = 1 m…