About Number Theory

Number Theory is one of the oldest mathematical disciplines. In fact, most mathematical subjects have been influenced by number theoretical ideas. Today, there are important applications, in particular to cryptography. Some of the famous and old problems have been solved recently. In 1995 A. Wiles and R. Taylor proved Fermat's Last Theorem. In May 2000 the Clay Institute offered prizes of $1.000.000 for the solution of any of seven well known problems. Two of these are about deep number theoretic questions, namely the Riemann Hypothesis and the Birch-Swinnerton-Dyer Conjecture. Moreover there is another award of $1.000.000 for the solution of Goldbach's Conjecture. This conjecture states that all even integers greater than two can be written as the sum of two primes.

In our research group we are concentrating on the following topics

• Arithmetical functions, for example mean value theorems, abstract analytic number theory, and recurrence sequences.
• Sieve methods and their applications to multiplicative and additive problems in number theory (such as the prime k-tuple conjecture or sums of unit fractions)
• Combinatorial Number Theory

Further Information:

• Staff, Addresses
• Recent Publications and Ph.D. Theses
• Lecture Notes
• Scientific Contacts

Misc:

• Workshop Analytische Zahlentheorie 04/2000 Goslar