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Kesava Menon, P.
- Interpolation Matrices and their Application to Group Representation
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Affiliations
1 Joint Cipher Bureau, Ministry of Defence, Sena Bhavan, New Delhi 110011, IN
1 Joint Cipher Bureau, Ministry of Defence, Sena Bhavan, New Delhi 110011, IN
Source
The Journal of the Indian Mathematical Society, Vol 38, No 1-4 (1974), Pagination: 399-403Abstract
The inversion of a matrix is, in general, a difficult problem involving calculations of several determinants and it is useful in practical applications to obtain parametric classes of matrices whose inverses could be obtained by simply changing the values of the parameters. The object of this paper is to consider such a class which is closely related to polynomial interpolation and to apply it to group representations.
- On the Sum Σ (a-1, n), [(a, n) = 1]
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Authors
Affiliations
1 Joint Cipher Bureau, Ministry of Defence, New Delhi, IN
1 Joint Cipher Bureau, Ministry of Defence, New Delhi, IN
Source
The Journal of the Indian Mathematical Society, Vol 29, No 3 (1965), Pagination: 155-163Abstract
The object of this paper is to establish a class of identities of which a typical one is
(l-l)
Σ (a-l,n ) = φ(n) d(n),
(a, n) = 1
where (m, n) denotes the g.e.d. of m and n,φ ¦n) is the number of numbers less than n and prime to n, d(n) is the number of divisors of n and the summition is over all residues a mod n that are prime to n.
- Series Associated with Ramanujan's Function T(n)
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Authors
Affiliations
1 A-46, D II Flats, Ring Road, Moti Bagh, New Delhi, IN
1 A-46, D II Flats, Ring Road, Moti Bagh, New Delhi, IN
Source
The Journal of the Indian Mathematical Society, Vol 27, No 2 (1963), Pagination: 57-65Abstract
In this paper we shall introduce a few other funotions involving T(n) and establish identities between them.- A Class of Quasi-Fields Having Isomorphic Additive &Multiplicative Groups
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Authors
Affiliations
1 A-46, D I I Flats, Ring Road, Moti Bagh, New Delhi, IN
1 A-46, D I I Flats, Ring Road, Moti Bagh, New Delhi, IN
Source
The Journal of the Indian Mathematical Society, Vol 27, No 2 (1963), Pagination: 71-90Abstract
By a quasi-field wo mean a set Q in which an addition and a multiplication are defined such that 1. Addition is an abelian group, 2. Multiplication is an abelian group, 3. The quasi-distributive law
a(b + c) + a = ab + ac
holds for all elements a, b, c ∈ Q.
- A Class of Linear Positive Operators
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Authors
Affiliations
1 A-45, D-II Flats, King Road, Moti Bagh, New Delhi, IN
1 A-45, D-II Flats, King Road, Moti Bagh, New Delhi, IN
Source
The Journal of the Indian Mathematical Society, Vol 26, No 1-2 (1962), Pagination: 77-80Abstract
For all functions f(x) bounded on the real axis and continuous in [ψ(0), ψ{a)], continuous on the right at ψ(a), and continuous on the left at ψ(0), the sequence {Ln(f; x)} converges uniformly f(ψ(x)) in [0, a].- On Vaidyanathaswamy's Class Division of the Residue Classes Modulo 'N'
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The Journal of the Indian Mathematical Society, Vol 26, No 3-4 (1962), Pagination: 167-186Abstract
Vaidyanathaswamy has shown that if the residue classes modulo N are separated into classes by putting all residues having the same greatest common divisor with N into one class, then the classes so obtained combine themselves by addition, that is to say, the aggregate formed by adding the residues of one class to those of another contain all the residues of any one class the same number of times.- On Gauss's Sums
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Authors
Affiliations
1 Ministry of Defence, New Delhi, IN
1 Ministry of Defence, New Delhi, IN
Source
The Journal of the Indian Mathematical Society, Vol 16 (1952), Pagination: 31-36Abstract
For integral values of a, x, M let us define the function F (a, x, M) by the relation
F(a, x, M) = ∑m(mod M) exp2πi/m(am2 + xm),
where Σ indicates summation over a complete set of residues m(mod M) modulo M.
- Some Generalizations of the Divisor Function
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The Journal of the Indian Mathematical Society, Vol 9 (1945), Pagination: 32-36Abstract
Let T(M1,...,Mr) represent the number of sets of divisors d1, . ...dr of M1 ..., Mr respectively such that the greatest common divisor of d1 ...,dr is unity.- A Generalization of Wilson's Theorem
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Authors
Affiliations
1 Madras Christian College, IN
1 Madras Christian College, IN
Source
The Journal of the Indian Mathematical Society, Vol 9 (1945), Pagination: 79-88Abstract
The object of this paper is to obtain a generalization of Wilson's theorem which includes as a particular case, Gauss's generalization.- Transformation of Products of υ-Functions
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Authors
Affiliations
1 Madras Christian College, IN
1 Madras Christian College, IN
Source
The Journal of the Indian Mathematical Society, Vol 9 (1945), Pagination: 93-105Abstract
We shall adopt the following well-known notations for υ-functions:
q = eπiτ, Imτ > o ;
υ2 (x|τ) = Σ q(n+1/2)2(2n+2)xπi,
υ (x|τ) = Σ qn2 e2nxπi,
υ (x|τ) = Σ (-I)nqn2 e2nπi.
Here, as well as in the sequel, Σ denotes summation over all integers from -∞ to +∞.
- Identities in Multiplicative Functions
Abstract Views :156 |
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Authors
Affiliations
1 Annamalai University, IN
1 Annamalai University, IN
Source
The Journal of the Indian Mathematical Society, Vol 7 (1943), Pagination: 58-62Abstract
Let λk(M)=kv, Ek(M)=kμ, where μ, v are respectively the number of distinct prime factors and the total number of prime factors of M. We shall denote E1(M) by E(M).- Multiplicative Functions which are Functions of the g.c.d. and l.c.m. of the Arguments
Abstract Views :138 |
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Authors
Affiliations
1 Annamalainagar, IN
1 Annamalainagar, IN
Source
The Journal of the Indian Mathematical Society, Vol 6 (1942), Pagination: 137-142Abstract
The object of this paper is to give generalizations of two of Dr. R. Vaidyanathaswamy's theorems on multiplicative functions which are functions of the greatest common divisor (g.c.d) and the least common multiple (l.c.m) of the arguments.- Transformations of Arithmetic Functions
Abstract Views :152 |
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Authors
Affiliations
1 Annamalai University, IN
1 Annamalai University, IN
Source
The Journal of the Indian Mathematical Society, Vol 6 (1942), Pagination: 143-152Abstract
An arithmetic function f(M1, M2,..., Mr) of r arguments is one which is defined for all non-zero positive integral values of the arguments M1, M2,..., Mr.- A Generalization of Legendre Functions
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Authors
Affiliations
1 University of Madras, IN
1 University of Madras, IN
Source
The Journal of the Indian Mathematical Society, Vol 5 (1941), Pagination: 92-102Abstract
When n is a positive integer, the differential equation admits of a polynomial solution and a non-polynomial solution, both of which have well-known properties.- A Theorem on Congruence
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Authors
Affiliations
1 Madras Christian College, IN
1 Madras Christian College, IN
Source
The Journal of the Indian Mathematical Society, Vol 2 (1937), Pagination: 332-333Abstract
The object of this note is to prove the following
THEOREM 1. Let p be an odd prime. Then
1p-1+2p-1+........+(p-1)p-1-p-(p-1)=0 (mod p2). (1)
1.1. The point in the above theorem is seen if we write the left side of (1) in the form
(1p-1-1)+(2p-1-1)+......+[(p-1)p-1-1]-[(p-1)+1]
which is=0 (mod p) by Fermat's and Wilson's theorems. The above theorem states that the left side of (1) is divisible by p2.
- On a Function of Ramanujan
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Φ(2s+1,x)=Σ((x+n+1)1/2-(x+n)1/2)2s+1=Σ((x+n+1)1/2+(x+n)1/2)-(2s+1) (s=1,2,3,...).
Authors
Affiliations
1 Cipher Bureaux, New Delhi, IN
1 Cipher Bureaux, New Delhi, IN
Source
The Journal of the Indian Mathematical Society, Vol 25, No 3-4 (1961), Pagination: 109-119Abstract
Ramanujan has obtained a formula for the functionΦ(2s+1,x)=Σ((x+n+1)1/2-(x+n)1/2)2s+1=Σ((x+n+1)1/2+(x+n)1/2)-(2s+1) (s=1,2,3,...).
- Summation of Certain Series
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φn=1/(1.2)n+1/(2.3)n+1/(3.4)n+...
can be summed in finite terms involving π for all positive integral values of n. In fact it can be shown to be equal to.
Authors
Affiliations
1 Cipher Bureaux, New Delhi, IN
1 Cipher Bureaux, New Delhi, IN
Source
The Journal of the Indian Mathematical Society, Vol 25, No 3-4 (1961), Pagination: 121-128Abstract
It does not appear to be known that the seriesφn=1/(1.2)n+1/(2.3)n+1/(3.4)n+...
can be summed in finite terms involving π for all positive integral values of n. In fact it can be shown to be equal to.