mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, Matsumoto zeta functions are a type of

zeta function In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function : \zeta(s) = \sum_^\infty \frac 1 . Zeta functions include: * Airy zeta function, related to the zeros of the Airy function * A ...

introduced by

Kohji Matsumoto is a Japanese number theorist. He is professor of mathematics at Nagoya University in Nagoya, Japan. Education and career Matsumoto graduated from the University of Tokyo in 1981. He got a doctoral degree from Rikkyo University in 1986, ad ...

in 1990. They are functions of the form :

\phi(s)=\prod_\frac

where ''p'' is a

prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

and ''A''_''p'' is a

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...

References

* Zeta and L-functions {{numtheory-stub