## Hankel determinants of zeta values.(English)Zbl 1387.11054

Summary: We study the asymptotics of Hankel determinants constructed using the values $$\zeta(an+b)$$ of the Riemann zeta function at positive integers in an arithmetic progression. Our principal result is a Diophantine application of the asymptotics.

### MSC:

 11J72 Irrationality; linear independence over a field 11M06 $$\zeta (s)$$ and $$L(s, \chi)$$ 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)

### Keywords:

irrationality; Hankel determinant; zeta value
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