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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…
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…
An Algebraic Generalization of the Ramanujan Sum
N. Uday Kiran
Ramanujan sums have attracted significant attention in both mathematical and engineering disciplines due to their diverse applications. In this paper, we introduce an algebraic gen…
An Algebraic Approach to Degenerate Bernoulli Numbers
N. Uday Kiran, Sampath Lonka
In this work we study the properties of a new algebraic variant of the degenerate Bernoulli polynomial and study the corresponding degenerate Bernoulli number $\…
An Algebraic Approach to q-Partial Fractions and Sylvester Denumerants
N. Uday Kiran
In 1857 Sylvester established an elegant theory that certain counting functions (which he termed denumerants) are quasi-polynomials by decomposing them into periodic and non-period…
Some Partial Fraction Identities associated with the Cyclotomic Polynomials
N. Uday Kiran
We establish some partial fraction identities for rational functions whose denominators are implicit products of the cyclotomic polynomials. To achieve this, we first develop a gen…