Prime numbers: the building blocks of numbers
Christoph Aistleitner, mathematician at TU Graz, is hot on the trail of vital information on the mystery of prime numbers.
For millennia, mathematicians have been fascinated by prime numbers – numbers, such as 2, 3, 5, 7 and so on, which are only divisible by themselves and one (4 and 6, for instance, are not prime numbers). Every whole number can be expressed as a product of prime numbers, so in a sense, prime numbers are the building blocks of which all other numbers are comprised.
The Riemann zeta (ζ) function provides mathematicians with a host of key information about prime numbers. The Riemann hypothesis, a conjecture about the positions at which the value of the zeta function is zero, has been considered the greatest unresolved problem in mathematics for more than a century. Although many of the world’s brightest mathematical minds are working on proving the hypothesis, and the Clay Mathematics Institute has offered prize money of USD 1 million to the first person to crack it, there is still no solution in sight.
Christoph AISTLEITNER
Assoc.Prof. Dipl.-Ing. Dr.techn.
TU Graz | Institute of Analysis and Number Theory
Phone: +43 316 873 7127
<link int-link-mail window for sending>aistleitner@math.tugraz.at
The Riemann zeta (ζ) function provides mathematicians with a host of key information about prime numbers. The Riemann hypothesis, a conjecture about the positions at which the value of the zeta function is zero, has been considered the greatest unresolved problem in mathematics for more than a century. Although many of the world’s brightest mathematical minds are working on proving the hypothesis, and the Clay Mathematics Institute has offered prize money of USD 1 million to the first person to crack it, there is still no solution in sight.
One step forward thanks to “unworkable” methods
A paper by Christoph Aistleitner of TU Graz’s Institute of Analysis and Number Theory, which won the Province of Styria’s 2017 research prize, has made an important new contribution to the debate on the behaviour of the Riemann zeta function. Although his findings do not reveal the positions at which the value of the function is zero, they do show how often the function has exceptionally high values. The results were published in<link https: link.springer.com article s00208-015-1290-0 _blank int-link-external external link in new> Mathematische Annalen, one of the leading mathematical research journals. The paper caused a stir around the world, as Aistleitner’s methodology was previously regarded by mathematics experts as “unworkable”.
Kontakt
Assoc.Prof. Dipl.-Ing. Dr.techn.
TU Graz | Institute of Analysis and Number Theory
Phone: +43 316 873 7127
<link int-link-mail window for sending>aistleitner@math.tugraz.at
