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E-book: Handbook of Number Theory I

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Covers a wealth of topics from number theory, with special attention given to estimates and inequalities. The most important results are presented, together with their refinements, extensions, or generalizations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross references provide new insight into fundamental research. For specialists in number theory as well as mathematicians in other fields of research who need access to some of these results. Annotation c. by Book News, Inc., Portland, Or.

This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.
Preface xxv
Basic Symbols 1(1)
Basic Notations 2(7)
Euler's ϕ-Function
9(30)
The Arithmetical Function d(n), its Generalizations and its Analogues
39(38)
Sum-of-Divisors Function, Generalizations, Analogues; Perfect Numbers and Related Problems
77(44)
P, p, B, β and Related Functions
121(34)
And Related Functions
155(32)
Function μ k-Free and k-Full Numbers
187(40)
Functions and the Sequence of Prime Numbers
227(48)
Primes in Arithmetic Progressions and Other Sequences
275(38)
Additive and Diophantine Problems Involving Primes
313(36)
Exponential Sums
349(40)
Character Sums
389(28)
Binomial Coefficients, Consecutive Integers and Related Problems
417(42)
Estimates Involving Finite Groups and Semi-Simple Rings
459(32)
Partitions
491(32)
Congruences, Residues and Primitive Roots
523(34)
Additive and Multiplicative Functions
557(54)
Index of Authors 611