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 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 (m ...
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.
Education
Helmut Maier graduated with a Diploma in Mathematics from the
University of Ulm
Ulm University (german: Universität Ulm) is a public university in Ulm, Baden-Württemberg, Germany. The university was founded in 1967 and focuses on natural sciences, medicine, engineering sciences, mathematics, economics and computer sci ...
in 1976, under the supervision of Hans-Egon Richert. He received his PhD from the
University of Minnesota
The University of Minnesota, formally the University of Minnesota, Twin Cities, (UMN Twin Cities, the U of M, or Minnesota) is a public land-grant research university in the Twin Cities of Minneapolis and Saint Paul, Minnesota, United States. ...
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
, mottoeng = "Arts, Knowledge, Truth"
, former_names = Catholepistemiad, or University of Michigania (1817–1821)
, budget = $10.3 billion (2021)
, endowment = $17 billion (2021)As o ...
University of Georgia
, mottoeng = "To teach, to serve, and to inquire into the nature of things.""To serve" was later added to the motto without changing the seal; the Latin motto directly translates as "To teach and to inquire into the nature of things."
, establ ...
. 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
Carl Bernard Pomerance (born 1944 in Joplin, Missouri) is an American number theorist. He attended college at Brown University and later received his Ph.D. from Harvard University in 1972 with a dissertation proving that any odd perfect number ...
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 E. Wirsing on this topic. He also collaborated with Hugh Lowell Montgomery on the size of the sum of the
Möbius function
The Möbius function 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 most of ...
Gérald Tenenbaum
Gérald Tenenbaum is a French mathematician and novelist, born in Nancy on 1 April 1952.Paul Erdős. Since 1993 Maier is a professor at the
University of Ulm
Ulm University (german: Universität Ulm) is a public university in Ulm, Baden-Württemberg, Germany. The university was founded in 1967 and focuses on natural sciences, medicine, engineering sciences, mathematics, economics and computer sci ...
, Germany.
Collaborators of Helmut Maier
include Paul Erdős, C. Feiler, John Friedlander, Andrew Granville, D. Haase, A. J. Hildebrand,
, J. W. Neuberger, A. Sankaranarayanan, A. Sárközy,
Wolfgang P. Schleich
Wolfgang P. Schleich (born 23 February 1957, in Mühldorf am Inn, Germany) is professor of theoretical physics and director of the quantum physics department at the University of Ulm.
Education, work and career
From 1980 to 1984, Schleich perform ...