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Creators/Authors contains: "Singha_Roy, Akash"

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  1. ; (, Proceedings of the Edinburgh Mathematical Society)
    Abstract We provide a uniform bound on the partial sums of multiplicative functions under very general hypotheses. As an application, we give a nearly optimal estimate for the count of$$n \le x$$for which the Alladi–Erdős function$$A(n) = \sum_{p^k \parallel n} k p$$takes values in a given residue class moduloq, whereqvaries uniformly up to a fixed power of$$\log x$$. We establish a similar result for the equidistribution of the Euler totient function$$\phi(n)$$among the coprime residues to the ‘correct’ moduliqthat vary uniformly in a similar range and also quantify the failure of equidistribution of the values of$$\phi(n)$$among the coprime residue classes to the ‘incorrect’ moduli. 
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    Free, publicly-accessible full text available February 10, 2026
  2. ; ; (, Michigan Mathematical Journal)
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  3. ; ; ; (, Proceedings of the American Mathematical Society)
    We provide a criterion to determine whether a real multiplicative function is a strong Benford sequence. The criterion implies that the k k -divisor functions, where k ≠<#comment/> 10 j k \neq 10^j , and Hecke eigenvalues of newforms, such as Ramanujan tau function, are strong Benford. In contrast to some earlier work, our approach is based on Halász’s Theorem. 
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  4. ; (, Canadian Mathematical Bulletin)
    Abstract We investigate the leading digit distribution of thekth largest prime factor ofn(for each fixed$$k=1,2,3,\dots $$) as well as the sum of all prime factors ofn. In each case, we find that the leading digits are distributed according to Benford’s law. Moreover, Benford behavior emerges simultaneously with equidistribution in arithmetic progressions uniformly to small moduli. 
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  5. ; (, Mathematische Zeitschrift)
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  6. ; (, Acta Arithmetica)
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