An Arithmetical Theory of Certain Numerical Functions (1915)

""An Arithmetical Theory of Certain Numerical Functions"" is a book written by Eric Temple Bell and published in 1915. The book focuses on the study of certain numerical functions and their properties using arithmetical methods. The functions discussed in the book include the divisor function, the sum-of-divisors function, the Euler phi function, the Mertens function, and the Liouville function. The book begins with an introduction to the theory of numbers and the basic concepts of arithmetical functions. The author then delves into the properties of the divisor function and its relation to prime numbers. The sum-of-divisors function is then discussed, followed by the Euler phi function and its applications to number theory. The latter part of the book focuses on the Mertens function and the Liouville function. The Mertens function is used to study the distribution of prime numbers, while the Liouville function is used to study the properties of quadratic residues. The book concludes with a discussion on the Riemann hypothesis and its relation to the functions studied in the book. Overall, ""An Arithmetical Theory of Certain Numerical Functions"" is a comprehensive and detailed study of various numerical functions and their applications to number theory. It is a valuable resource for mathematicians and researchers interested in the field of number theory.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.