Titlebook: Number Theory; R. P. Bambah,V. C. Dumir,R. J. Hans-Gill Book 2000 Hindustan Book Agency 2000

率直

Recent Developments in the Mean Square Theory of the Riemann Zeta and Other Zeta-Functions,spects of the theory of zeta-functions, such as the distribution of zeros, value-distribution, and applications to number theory. Some of them are probably treated in the articles of Professor Apostol and Professor Ramachandra in the present volume.

Androgen

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. It can be stated in various equivalent forms, two of which are: . and

無(wú)脊椎

craven

On Values of Linear and Quadratic Forms at Integral Points,The aim of this article is to give an exposition of certain applications of the study of the homogeneous space .(.)/.(.) and the flows on it induced by subgroups of .(.), to problems on values of linear and quadratic forms at integral points. Also, some complements to Margulis’s theorem on Oppenheim’s conjecture are proved.

surmount

oxidant

指耕作

,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.

insipid

Continuous Homomorphisms as Arithmetical Functions, and Sets of Uniqueness,Let, as usual ?, ?, ?, ?, ? be the set of positive integers, integers, rational, real, and complex numbers, respectively. Let ?., ?. be the multiplicative group of positive rationals, reals, respectively. Let . be the set of prime numbers.

乏味

柏樹