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math.NT2025
On Some Generalisations of Gauss Sequences
Sathyanarayan Narayan, N. Uday Kiran
In this paper, we introduce integer sequences satisfying new congruence properties inspired by the Euler and Gauss congruences, which we call Euler--Gauss sequences. Noting that ev…
math.NT2025
Some Generalizations of Totient Function with Elementary Symmetric Sums
Udvas Acharjee, N. Uday Kiran
We generalize certain totient functions using elementary symmetric polynomials and derive explicit product forms for the totient functions involving the second elementary symmetric…
math.GM2025
Further Generalization of Ramanujan Sums with Regular A-Functions
Udvas Acharjee, N. Uday Kiran
In the study of Ramanujan sums, the so-called regular -function is a set-valued multiplicative function that tracks certain subsets of the divisor sets of natural numbers. McCar…