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Artins Primitive Root Conjecture

Name: Artins Primitive Root Conjecture
Brand: VDM Verlag Dr. Mueller E.K.
SKU: 06817853
Price: 20014 HUF
Availability: InStock
Author: Sourav Sen Gupta
ISBN: 9783639086935

Sourav Sen Gupta

Language

English

Book Paperback

Libristo code: 06817853

Publishers VDM Verlag Dr. Mueller E.K., October 2008

This book explores the different approaches towards§proving Artin''s ''primitive root'' conjecture§u... Full description

Libristo code: 06817853

134 b

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This book explores the different approaches towards§proving Artin''s ''primitive root'' conjecture§unconditionally and the elliptic curve analogue of§the same. The conjecture was posed by E. Artin in§1927, and it still remains an open problem. In 1967,§C. Hooley proved the conjecture based on the§assumption of the generalized Riemann hypothesis.§Thereafter, the mathematicians tried to get rid of§the assumption and it seemed quite a daunting task.§The best results we have so far are by R. Gupta and§M. Ram Murty (1983), and D. R. Heath-Brown (1986). It§states that there can be at most 12 exceptional§integers or at most 2 exceptional primes for which§the conjecture does not hold. But the question -§''Which ones?'', remains illusive. The first part of§this book deals with these sieve theoretic results by§Gupta-Murty and Heath-Brown. The second half§discusses the elliptic curve analogue of the§conjecture which was proposed by Lang and Trotter in§1977 and was proved by Gupta and Murty in 1986,§assuming the generalized Riemann hypothesis, for§curves with complex multiplication. These discussions§will help the reader gain a broad perspective of the§conjecture and the current advancements.