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Titlebook: Number Theory; R. P. Bambah,V. C. Dumir,R. J. Hans-Gill Book 2000 Springer Basel AG 2000 algebra.arithmetic.boundary element method.crypto

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A Centennial History of the Prime Number Theorem,Among the thousands of discoveries made by mathematicians over the centuries, some stand out as significant landmarks. One of these is the ., which describes the asymptotic distribution of prime numbers.
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On the Oscillation Theorems of Pringsheim and Landau,Our theme is a relation between the sign of a real function and the analytic behaviour of its associated generating function at a special point on the boundary of convergence.
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The ,-conjecture,In the present paper we give a survey of the .-conjecture and of its modifications and generalizations. We discuss several consequences of the conjecture. At the end of the paper there are given numerical examples giving some evidence for the conjecture.
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,Artin’s Conjecture for Polynomials Over Finite Fields,A classical conjecture of E. Artin[Ar] predicts that any integer . ≠ ±1 or a perfect square is a primitive root (mod .) for infinitely many primes .. This conjecture is still open. In 1967, Hooley[H] proved the conjecture assuming the (as yet) unresolved generalized Riemann hypothesis for Dedekind zeta functions of certain number fields.
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