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 Diric ...

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 Maier's matrix method is a technique in analytic number theory due to Helmut Maier that is used to demonstrate the existence of intervals of natural numbers within which the prime numbers are distributed with a certain property. In particular it ha ...

as well as

Maier's theorem In number theory, Maier's theorem is a theorem about the numbers of primes in short intervals for which Cramér's probabilistic model of primes gives a wrong answer. The theorem states that if π is the prime-counting function and λ is greater ...

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 \operatorname(s) > ...

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 university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Tw ...

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

. 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 ...

and the

Institute for Advanced Study, Princeton The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

, Maier obtained a permanent position at the

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 h ...

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 Sergei Vladimirovich Konyagin (russian: Серге́й Владимирович Конягин; born 25 April 1957) is a Russian mathematician. He is a professor of mathematics at the Moscow State University. Konyagin participated in the Internat ...

and E. Wirsing on this topic. He also collaborated with

Hugh Lowell Montgomery Hugh Lowell Montgomery (born August 26, 1944) is an American mathematician, working in the fields of analytic number theory and mathematical analysis. As a Marshall scholar, Montgomery earned his Ph.D. from the University of Cambridge. For many ...

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 oft ...

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 ...

. Maier and

Gérald Tenenbaum Gérald Tenenbaum is a French mathematician and novelist, born in Nancy on 1 April 1952.Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 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 ...

. Since 1993 Maier is a professor at the

, Germany. Collaborators of Helmut Maier include

Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 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 ...

, C. Feiler,

John Friedlander John Friedlander is a Canadian mathematician specializing in analytic number theory. He received his B.Sc. from the University of Toronto in 1965, an M.A. from the University of Waterloo in 1966, and a Ph.D. from Pennsylvania State University i ...

, 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 ...

Cameron Leigh Stewart Cameron Leigh Stewart FRSC is a Canadian mathematician. He is a professor of pure mathematics at the University of Waterloo. Contributions He has made numerous contributions to number theory, in particular to work on the ''abc'' conjecture. In ...

References

External links

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

Education

Research and academic positions

See also

References

External links