Author
V. Kumar Murty
Other affiliations: Concordia University, Institute for Advanced Study, Tata Institute of Fundamental Research ...read more
Bio: V. Kumar Murty is an academic researcher from University of Toronto. The author has contributed to research in topics: Ramanujan's sum & Abelian group. The author has an hindex of 21, co-authored 123 publications receiving 1377 citations. Previous affiliations of V. Kumar Murty include Concordia University & Institute for Advanced Study.
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161 citations
Book•
01 Jan 1997
TL;DR: This book systematically develops some methods for proving the non-vanishing of certain L-functions at points in the critical strip.
Abstract: Award-winning monograph of the Ferran Sunyer i Balagure Prize 1996. This book systematically develops some methods for proving the non-vanishing of certain L-functions at points in the critical strip. Researchers in number theory, graduate students who wish to enter into the area and non-specialists who wish to acquire an introduction to the subject will benefit by a study of this book. One of the most attractive features of the monograph is that it begins at a very basic level and quickly develops enough aspects of the theory to bring the reader to a point the latest discoveries as are presented in the final chapters can be fully appreciated.
127 citations
TL;DR: Gauthier-Villars as discussed by the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).
Abstract: © Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1992, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www. elsevier.com/locate/ansens) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
77 citations
TL;DR: Three refinements to Miller's algorithm are given, one of which is especially efficient when the underlying elliptic curve is over a finite field of characteristic three, which is a case of particular cryptographic interest.
64 citations
Posted Content•
TL;DR: In this paper, three refinements to Miller's algorithm for computing Weil/Tate Pairing were proposed and they achieved the optimal behavior if the binary expansion of the involved integer has more zeros.
Abstract: In this paper we propose three refinements to Miller’s algorithm for computing Weil/Tate Pairing. The first one is an overall improvement and achieves its optimal behavior if the binary expansion of the involved integer has more zeros. If more ones are presented in the binary expansion, second improvement is suggested. The third one is especially efficient in the case base three. We also have some performance analysis. keywords: algorithm, elliptic curve, cryptography, Weil/Tate pairing
63 citations
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Book•
01 Jan 1971
TL;DR: The cohomology group assoicated with cusp forms and arithmetic Fuschian groups of the first kind was introduced in this paper..., where we have shown that it is possible to construct an algebraic algebraic curve and a complex multiplication of elliptic curves.
Abstract: * uschian groups of the first kind * Automorphic forms and functions * Hecke operators and the zeta-functions associated with modular forms * Elliptic curves * Abelian extensions of imaginary quadratic fields and complex multiplication of elliptic curves * Modular functions of higher level * Zeta-functions of algebraic curves and abelian varieties * The cohomology group assoicated with cusp forms * Arithmetic Fuschian groups
1,146 citations
949 citations
TL;DR: The complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry can be found in this paper, where the authors provide a good introduction to the subject.
Abstract: Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.
699 citations
TL;DR: In this article, the authors give a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients, and their study has developed into a fertile and extensive theory enriching many branches of pure mathematics.
Abstract: First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.
644 citations