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Some New Applications of the Mellin Transform Involving the Lambert Transforms and Implications for the Riemann Hypothesis
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Some New Applications of the Mellin Transform Involving the Lambert Transforms and Implications for the Riemann Hypothesis
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Journal Article
Some New Applications of the Mellin Transform Involving the Lambert Transforms and Implications for the Riemann Hypothesis
2025
Overview
This work investigates the interplay between the Mellin transform and Lambert transforms to derive several novel results. In particular, we establish new inversion formulae for the Lambert transforms along with a Plancherel-type identity. Additionally, we explore the implications of these findings, highlighting their relevance to Salem’s equivalence and potential connections with the Riemann hypothesis.
Publisher
MDPI AG
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