Upper bounds for fractional joint moments of the Riemann zeta function

Michael J. Curran Acta Arithmetica MSC: Primary 11M06; Secondary 11M50. DOI: 10.4064/aa220127-11-4 Published online: 23 May 2022


We establish upper bounds for the joint moments of the $2k$th power of the Riemann zeta function with the $2h$th power of its derivative for $0 \leq h \leq 1$ and $1\leq k \leq 2$. These bounds are expected to be sharp based upon predictions from random matrix theory.


  • Michael J. CurranMathematical Institute
    University of Oxford
    OX2 6GG Oxford, United Kingdom

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