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Elementary and Analytic Theory of Algebraic Numbers
1. Dedekind Domains and Valuations.- 2. Algebraic Numbers and Integers.- 3. Units and Ideal Classes.- 4. Extensions.- 5. P-adic Fields.- 6. Applications of the Theory of P-adic Fields.- 7. Analytical
On Sums of Units
Abstract.It is shown that if R is a finitely generated integral domain of zero characteristic, then for every n there exist elements of R which are not sums of at most n units. This applies in
The Development of Prime Number Theory: From Euclid To Hardy And Littlewood
1. Early Times.- 2. Dirichlet's Theorem on Primes in Arithmetic Progressions.- 3. ?ebysev's Theorem.- 4. Riemann's Zeta-function and Dirichlet Series.- 5. The Prime Number Theorem.- 6. The Turn of
Uniform Distribution of Sequences of Integers in Residue Classes
General results.- Polynomial sequences.- Linear recurrent sequences.- Additive functions.- Multiplicative functions.- Polynomial-like functions.
Units in residue classes
A note on Artin's conjecture in algebraic number fields.
L Recently R. Gupta, M. Ram Murty [2] and D. R. Heath-Brown [3] established the truth of the qualitative form of Artin's conjecture about primitive roots for a majority of rational integers. (This