Create Publications “2025-10-08-a-remark-on-weighted-average-multiplicities-in-prime-factorisation”

Author: cb580

_publications/2025-10-08-a-remark-on-weighted-average-multiplicities-in-prime-factorisation.md

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+---
+layout: publication-single
+title: A remark on weighted average multiplicities in prime factorisation
+abstract: We study a generalisation of the quality of an ABC triple that we call
+  the weighted average multiplicity (WAM), in which the logarithmic heights of
+  prime factors are raised to a complex exponent s. The WAM is connected to the
+  standard ABC conjecture at s = 1. We show that for real part of s less than 1,
+  WAM is unbounded over ABC triples both for integers and polynomials. For real
+  part greater than 1, we characterise a boundary beyond which WAM is
+  holomorphic and bounded. In this region, we show that WAM is related to the
+  multiplicity of the largest prime factor of the triple, a quantity that we
+  connect with the original ABC conjecture and whose distribution we explore
+  computationally.
+published: 2025-10-08
+authors:
+  internal_authors:
+    - Challenger Mishra
+    - Daattavya Aggarwal
+  external_authors:
+    - family: Mirjanić
+      given: "Viktor "
+details:
+  pdf: https://arxiv.org/pdf/2510.06993
+---