An Introduction to the Theory of the Riemann Zeta-Function (Cambridge Studies in Advanced Mathematics)

This Is A Modern Introduction To The Analytic Techniques Used In The Investigation Of Zeta Functions, Through The Example Of The Riemann Zeta Function. Riemann Introduced This Function In Connection With His Study Of Prime Numbers And From This Has Developed The Subject Of Analytic Number Theory. Since Then Many Other Classes Of 'zeta Function' Have Been Introduced And They Are Now Some Of The Most Intensively Studied Objects In Number Theory. Professor Patterson Has Emphasised Central Ideas Of Broad Application, Avoiding Technical Results And The Customary Function-theoretic Approach. Thus, Graduate Students And Non-specialists Will Find This An Up-to-date And Accessible Introduction, Especially For The Purposes Of Algebraic Number Theory. There Are Many Exercises Included Throughout, Designed To Encourage Active Learning. S.j. Patterson. Includes Index. Bibliography: P. [152]-154.

This is a modern introduction to the analytic techniques used in the investigation of zeta-function. Riemann introduced this function in connection with his study of prime numbers, and from this has developed the subject of analytic number theory. Since then, many other classes of "zeta-function" have been introduced and they are now some of the most intensively studied objects in number theory. Professor Patterson has emphasized central ideas of broad application, avoiding technical results and the customary function-theoretic approach.

In this chapter it will be shown how the Poisson Summation Formula leads to the functional equation for the zeta-function.