Ling 310, adapted from umass ling 409, partee lecture notes march 1, 2006 p. In number theory, an arithmetic, arithmetical, or numbertheoretic function is for most authors any function f n whose domain is the positive integers and whose range is a subset of the complex numbers. Number theoretic functions international journal of mathematics. A function fx is called a periodical function if there exists a constant num ber t, t. This is a listing of articles which explain some of these functions in more detail. Truncations of the ring of numbertheoretic functions snellman, jan, homology, homotopy and applications, 2000 a characterization of rings of density continuous functions. A characterization of rings of density continuous functions. In number theory, an arithmetic, arithmetical, or numbertheoretic function is for most authors any function fn whose domain is the positive integers and whose range is a subset of the complex numbers. All these functions play very important role in the field of number theory. Two important numbertheoretic functions are eulers function. Chapter 7 eulers generalization of fermats theorem. You can perform elementary numbertheoretic operations to find the lcm, gcd, modulus, quotient, and remainder.
Truncations of the ring of numbertheoretic functions snellman, jan, homology, homotopy and applications, 2000. Multiplicative number theoretic functions mathematics. This set of notes on number theory was originally written in 1995 for students. Pdf some remarks concerning the number theoretic functions. American river software elementary number theory, by. Until now the approximation of individual real numbers has been studied with the help of integers, and for this the methods of analysis and geometry have been. A modern, abstract point of view contrasts large function spaces, which are infinitedimensional and. The ring of numbertheoretic functions mathematical sciences. Number theory modular arithmetic operations and sequences of numbers you can perform elementary numbertheoretic operations to find the lcm, gcd, modulus, quotient, and remainder. Analytic number theoryformulas for numbertheoretic functions. Introduction to analytic number theory department of mathematics. There are several important arithmetic functions, of which three are pre.
You also can find prime numbers, and special sequences of numbers, such as harmonic, bernoulli, and euler numbers. By the fundamental theorem of arithmetic, n is divisible by some prime p. Basic concepts of set theory, functions and relations. Padic numbers, padic analysis and zetafunctions, 2nd edn. An arithmetic function is a mapping from the positive in tegers into the field of complex numbers. In mathematics, some functions or groups of functions are important enough to deserve their own names. Core function based characterizations of number theoretic. Transcendence of power series for some number theoretic. There is a large theory of special functions which developed out of statistics and mathematical physics. On periodicity of trigonometric functions and connections.