I’m back in Antwerp for over a week now, and finally got hold of our copy of Shimura’s “Introduction to the arithmetic theory of automorphic functions”. The sad story of disappearing libraries at our university, and possibly elsewhere (everywhere?). Over 20 years ago our maths department shared a building with the language departments, as well […]

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Academics / Mathematics : Programming Praxis

In the last several exercises we have been building a library of functions for dealing with big integers. Our library supports basic predicates and comparisons, the four basic arithmetic operations, and input and output. Now is a go...

Academics / Mathematics : Terence Tao's Blog

Analytic number theory is often concerned with the asymptotic behaviour of various arithmetic functions: functions or from the natural numbers to the real numbers or complex numbers. In this post, we will focus on the purely algebra...

Academics / Mathematics : Terence Tao's Blog

In analytic number theory, it is a well-known phenomenon that for many arithmetic functions of interest in number theory, it is significantly easier to estimate logarithmic sums such as than it is to estimate summatory functions suc...

Academics / Mathematics : Terence Tao's Blog

A basic object of study in multiplicative number theory are the arithmetic functions: functions from the natural numbers to the complex numbers. Some fundamental examples of such functions include The constant function ; The Kroneck...

Academics / Mathematics : Terence Tao's Blog

In analytic number theory, an arithmetic function is simply a function from the natural numbers to the real or complex numbers. (One occasionally also considers arithmetic functions taking values in more general rings than or, as in...

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