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Pointwise convergence of bilinear polynomial averages over the primes

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Pointwise convergence occurs almost everywhere for non-conventional ergodic averages involving bilinear polynomials.
Key findings indicate that averages converge for functions in Lp spaces under specific conditions on the polynomial degrees.
The methodology employs estimates from previous works and extends them into the realm of polynomial averages tied to the von Mangoldt function.
This work bridges previous results with Gowers norm techniques, highlighting significant insights into bilinear forms.

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Analysis demonstrates pointwise convergence of ergodic averages in measure-preserving systems, suggesting new weight applications.

Krause et al. (2025) studied this question.

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