Looking for a specific product?

Make a search for products & suppliers, articles & news.

Finalist: Ane Espeseth og Torstein Vik

Ane Espeseth (18 år) og Torstein Vik (16 år), Ålesund
Skole: Fagerlia videregående skole

Motivic Symbols and Classical Multiplicative Functions


f we take two integers (also known as whole numbers), we can add them, subtract one from the other, or multiply them. For example:

5 + 3 = 8     5 - 3 = 2     5*3 = 15

In addition to these three operations, we have another one, very useful when computing probabilities, known as a binomial coecient. A binomial coecient
will take a positive integer, for instance 5, and another integer, for instance 3,
and compute how many di erent ways you can choose 3 things out of 5 things.
A computation would look like this:






This answer tells us that if we must choose 3 students out of a group of 5 students, there are 10 possible choices.

These four operations are related by certain formulas, called lambda-ring axioms. Any "number system" which has four operations related to each other by these axioms is called a lambda-ring.

The first main discovery in our report is a method for constructing infinitely many new "number systems" like this, which are almost as easy to compute with as the integers. The method is built on a technical new idea called a motivic symbol.

A completely different area of mathematics is the study of prime numbers. A prime number is a positive integer that cannot be factored into two smaller positive integers. For example, 7 is a prime number, but 8 is not, since it can be factored into 2 times 4. Understanding the structure of the prime numbers is one of most dicult challenges in all of mathematics. To help in this endeavour,  mathematicians have invented something called multiplicative functions. A typical example is the sigma function, which computes the sum of all factors of a given number.

Many of the most important multiplicative functions can be expressed in terms of the famous Riemann zeta function by a speci c kind of formula. Such functions are called classical in our report.

Now we can formulate our second main discovery, which is a new and surprising connection between the theory of lambda-rings and the theory of multiplicative functions. We have proved that the collection of classical  multiplicative functions is a lambda-ring, in which the operations correspond to certain well-known  number-theoretic operations on multiplicative functions. For example, addition in this lambda-ring corresponds to an operation called Dirichlet


Related news

Latest news

First phase of DNV GL led offshore cable and pipeline operations equipment joint industry project completed

The data analysed during phase 1 has identified and recorded various processes...

The end of the paper chase: DNV GL to roll out electronic certificates across entire fleet

Certificates are published on DNV GL’s customer portal immediately after an onboard survey is completed,

New Integrated Solution Set to Redefine DP Reference Systems

DPS i2 and DPS i4 utilise KONGSBERG's unique motion gyro compass (MGCTM) and motion reference unit (MRUTM) technology.

Servogear service hub in Asia

September 2017, Servogear announce the strengthening of our presence in Asia with the establishment of a service hub in Singapore.

New Machining Center In Fredrikstad

Jotne opened a brand new machining hall in Fredrikstad on the 20th of May.

Construction and Testing of 4 Caterpillar C280 Gensets Finalized

Jotne has together with thier client Pon Power finalized construction and testing of 4 Caterpillar C280 gensets in Jotne’s factory in Fredrikstad. 

DNV GL acquires specialist in CFD for fire and explosion analysis, ComputITG

With its roots in the offshore sector,

New land based contract with Sisomar

Sisomar’s philosophy is close to AKVA group’s underlying strategy to develop technological solutions based on good fish health and solid biology. 

Geothermal energy- an answer for selected areas in Poland

During the last weeks the experts have visited the selected sites in Poland and also been on a study visit to Iceland.