Metrical Properties for the Weighted Products of Multiple Partial Quotients in Continued Fractions

The research of A. Bakhtawar is supported by the ARC grant DP180100201, of M. Hussain by the ARC grant DP200100994, of D. Kleinbock by the NSF grant DMS-1900560, and of B. Wang by NSFC (11831007). Part of this work was carried out during the workshop "Ergodic Theory, Diophantine approximation and related topics" sponsored by the MATRIX Research Institute.