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14 papers
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…
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…
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…
Global Wellposedness of a Class of Weakly Hyperbolic Cauchy Problems with Variable Multiplicities on
Sandro Coriasco, Giovanni Girardi, N. Uday Kiran
We study a class of weakly hyperbolic Cauchy problems on , involving linear operators with characteristics of variable multiplicities, whose coefficients are unbounde…
The Restricted Partition and q-Partial Fractions
N. Uday Kiran
The restricted partition function counts the partitions of into at most parts. In the nineteenth century Sylvester showed that these partitions can be expressed…
Global Well-posedness of a Class of Singular Hyperbolic Cauchy Problems
Rahul Raju Pattar, N. Uday Kiran
The goal of this paper is to establish a global well-posedness, cone condition and loss of regularity for singular hyperbolic equations with coefficients in { $L^1((0,T];C^\infty(\…
Global Well-Posedness of a Class of Hyperbolic Cauchy Problems with Coefficients Sublogarithmic in Time
Rahul Raju Pattar, N. Uday Kiran
The goal of this paper is to study global well-posedness, cone of dependence and loss of regularity of the solutions to a class of strictly hyperbolic equations with coefficients d…
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 $\…
Energy Estimates and Global Well-posedness for a Broad Class of Strictly Hyperbolic Cauchy Problems with Coefficients Singular in Time
Rahul Raju Pattar, N. Uday Kiran
The goal of this paper is to establish a global well-posedness for a broad class of strictly hyperbolic Cauchy problems with coefficients in gro…
Strictly Hyperbolic Cauchy Problems on with Unbounded and Singular Coefficients
Rahul Raju Pattar, N. Uday Kiran
We investigate the behavior of the solutions of a class of certain strictly hyperbolic equations defined on in relation to a class of metrics on the phas…
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…
Global Well-Posedness of a Class of Strictly Hyperbolic Cauchy Problems with Coefficients Non-Absolutely Continuous in Time
Rahul Raju Pattar, N. Uday Kiran
We investigate the behavior of the solutions of a class of certain strictly hyperbolic equations defined on in relation to a class of metrics on the phase space.…
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…