Gopalakrishna Gadiyar - Academia.edu (original) (raw)
Theoretical and mathematical physicist
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Papers by Gopalakrishna Gadiyar
In this note we try to bring out the ideas of Hamming's classic paper on coding theory in a form ... more In this note we try to bring out the ideas of Hamming's classic paper on coding theory in a form understandable by undergraduate students of mathematics.
In this note we try to bring out the ideas of Hamming's classic paper on coding theory in a form ... more In this note we try to bring out the ideas of Hamming's classic paper on coding theory in a form understandable by undergraduate students of mathematics.
We have gone back to old methods found in the historical part of Hardy's Divergent Series wel... more We have gone back to old methods found in the historical part of Hardy's Divergent Series well before the invention of the modern analytic continuation to use formal manipulation of harmonic sums which produce some interesting formulae. These are linear recurrence relations for ∑_n=1^∞ H_n n^k which in turn yield linear recurrence relations for ζ '(-k) and hence using the functional equation to a linear recurrence relation for ζ '(2k) and ζ (2k+1). Questions of rigor have been postponed to a subsequent preprint.
We show that the classical discrete logarithm problem over prime fields can be reduced to that of... more We show that the classical discrete logarithm problem over prime fields can be reduced to that of solving a system of linear modular equations.
arXiv: Number Theory, 2012
Classically, Euler developed the theory of the Riemann zeta - function using as his starting poin... more Classically, Euler developed the theory of the Riemann zeta - function using as his starting point the exponential and partial fraction forms of cot(z) . In this paper we wish to develop the theory of LLL-functions of elliptic curves starting from the theory of elliptic functions in an analogous manner.
We have gone back to old methods found in the historical part of Hardy’s Divergent Series well be... more We have gone back to old methods found in the historical part of Hardy’s Divergent Series well before the invention of the modern analytic continuation to use formal manipulation of harmonic sums which produce some interesting formulae. These are linear recurrence relations for ∞ ∑ n=1 Hnn k which in turn yield linear recurrence relations for ζ(−k) and hence using the functional equation to a linear recurrence relation for ζ(2k) and ζ(2k + 1). Questions of rigor have been postponed to a subsequent preprint.
ArXiv, 2016
We show that the classical discrete logarithm problem over prime fields can be reduced to that of... more We show that the classical discrete logarithm problem over prime fields can be reduced to that of solving a system of linear modular equations.
In this note we give an algorithm to explicitly construct the modular parametrization of an ellip... more In this note we give an algorithm to explicitly construct the modular parametrization of an elliptic curve over the rationals given the Weierstrass function wp(z)\wp (z)wp(z).
Czechoslovak Mathematical Journal
In this brief note we connect the discrete logarithm problem over prime fields in the safe prime ... more In this brief note we connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.
Indian Journal of Pure and Applied Mathematics, 2014
Czechoslovak Mathematical Journal, 2014
Czechoslovak Mathematical Journal, 2014
In this note we try to bring out the ideas of Hamming's classic paper on coding theory in a form ... more In this note we try to bring out the ideas of Hamming's classic paper on coding theory in a form understandable by undergraduate students of mathematics.
In this note we try to bring out the ideas of Hamming's classic paper on coding theory in a form ... more In this note we try to bring out the ideas of Hamming's classic paper on coding theory in a form understandable by undergraduate students of mathematics.
We have gone back to old methods found in the historical part of Hardy's Divergent Series wel... more We have gone back to old methods found in the historical part of Hardy's Divergent Series well before the invention of the modern analytic continuation to use formal manipulation of harmonic sums which produce some interesting formulae. These are linear recurrence relations for ∑_n=1^∞ H_n n^k which in turn yield linear recurrence relations for ζ '(-k) and hence using the functional equation to a linear recurrence relation for ζ '(2k) and ζ (2k+1). Questions of rigor have been postponed to a subsequent preprint.
We show that the classical discrete logarithm problem over prime fields can be reduced to that of... more We show that the classical discrete logarithm problem over prime fields can be reduced to that of solving a system of linear modular equations.
arXiv: Number Theory, 2012
Classically, Euler developed the theory of the Riemann zeta - function using as his starting poin... more Classically, Euler developed the theory of the Riemann zeta - function using as his starting point the exponential and partial fraction forms of cot(z) . In this paper we wish to develop the theory of LLL-functions of elliptic curves starting from the theory of elliptic functions in an analogous manner.
We have gone back to old methods found in the historical part of Hardy’s Divergent Series well be... more We have gone back to old methods found in the historical part of Hardy’s Divergent Series well before the invention of the modern analytic continuation to use formal manipulation of harmonic sums which produce some interesting formulae. These are linear recurrence relations for ∞ ∑ n=1 Hnn k which in turn yield linear recurrence relations for ζ(−k) and hence using the functional equation to a linear recurrence relation for ζ(2k) and ζ(2k + 1). Questions of rigor have been postponed to a subsequent preprint.
ArXiv, 2016
We show that the classical discrete logarithm problem over prime fields can be reduced to that of... more We show that the classical discrete logarithm problem over prime fields can be reduced to that of solving a system of linear modular equations.
In this note we give an algorithm to explicitly construct the modular parametrization of an ellip... more In this note we give an algorithm to explicitly construct the modular parametrization of an elliptic curve over the rationals given the Weierstrass function wp(z)\wp (z)wp(z).
Czechoslovak Mathematical Journal
In this brief note we connect the discrete logarithm problem over prime fields in the safe prime ... more In this brief note we connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.
Indian Journal of Pure and Applied Mathematics, 2014
Czechoslovak Mathematical Journal, 2014
Czechoslovak Mathematical Journal, 2014