Helmut Maier (born 17 October 1953) is a German mathematician and professor at the University of Ulm, Germany. He is known for his contributions in

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dir ...

and

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...

and particularly for the so-called Maier's matrix method as well as Maier's theorem for primes in short intervals. He has also done important work in exponential sums and trigonometric sums over special sets of integers and the

Riemann zeta function The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for and its analytic c ...

Education

Helmut Maier graduated with a Diploma in Mathematics from the University of Ulm in 1976, under the supervision of Hans-Egon Richert. He received his PhD from the

University of Minnesota The University of Minnesota Twin Cities (historically known as University of Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Twin Cities of Minneapolis and Saint ...

in 1981, under the supervision of J. Ian Richards.

Research and academic positions

Maier's PhD thesis was an extension of his paper ''Chains of large gaps between consecutive primes''. In this paper Maier applied for the first time what is now known as Maier's matrix method. This method later on led him and other mathematicians to the discovery of unexpected irregularities in the distribution of prime numbers. There have been various other applications of Maier's Matrix Method, such as on irreducible polynomials and on strings of consecutive primes in the same residue class. After postdoctoral positions at the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

and the Institute for Advanced Study, Princeton, Maier obtained a permanent position at the

University of Georgia The University of Georgia (UGA or Georgia) is a Public university, public Land-grant university, land-grant research university with its main campus in Athens, Georgia, United States. Chartered in 1785, it is the oldest public university in th ...

. While in Georgia he proved that the usual formulation of the Cramér model for the distribution of prime numbers is wrong. This was a completely unexpected result. Jointly with Carl Pomerance he studied the values of Euler's -function and large gaps between primes. During the same period Maier investigated as well the size of the coefficients of cyclotomic polynomials and later collaborated with Sergei Konyagin and Eduard Wirsing on this topic. He also collaborated with Hugh Lowell Montgomery on the size of the sum of the

Möbius function The Möbius function \mu(n) is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also transliterated ''Moebius'') in 1832. It is ubiquitous in elementary and analytic number theory and m ...

under the assumption of the

Riemann Hypothesis In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in pure ...

. Maier and Gérald Tenenbaum in joint work investigated the sequence of divisors of integers, solving the famous ''propinquity'' problem of

Paul Erdős Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, g ...

. Since 1993, Maier has been a professor at the University of Ulm, Germany. Collaborators of Helmut Maier include

, C. Feiler, John Friedlander, Andrew Granville, D. Haase, A. J. Hildebrand, , J. W. Neuberger, A. Sankaranarayanan, A. Sárközy, Wolfgang P. Schleich, Cameron Leigh Stewart.

References

External links

Maier's webpage
{{DEFAULTSORT:Maier, Helmut 20th-century German mathematicians 21st-century German mathematicians German number theorists University of Minnesota alumni Academic staff of the University of Ulm Living people 1953 births

Education

Research and academic positions

See also

References

External links