A paucity problem associated with a shifted integer analogue of the divisor function

@article{Heap2021APP,
  title={A paucity problem associated with a shifted integer analogue of the divisor function},
  author={Winston Heap and Anurag Sahay and Trevor D. Wooley},
  journal={Journal of Number Theory},
  year={2021}
}

Paucity phenomena for polynomial products

. Let P ( x ) ∈ Z [ x ] be a polynomial with at least two distinct complex roots. We prove that the number of solutions ( x 1 , . . . , x k , y 1 , . . . , y k ) ∈ [ N ] 2 k to the equation Y 1 ≤ i ≤

Moments of the Hurwitz zeta function on the critical line

. We study the moments M k ( T ; α ) = 2 T T | ζ s, α ) | 2 k dt of the Hurwitz zeta function ζ ( s, α ) on the critical line, s = 1 / 2+ it with a rational shift α ∈ Q . We conjecture, in analogy

THE PAUCITY PROBLEM FOR CERTAIN SYMMETRIC DIOPHANTINE EQUATIONS

  • T. Wooley
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 2022
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