What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Number theory
- Algebra
Pure mathematics, Mathematical analysis, Riemann zeta function, Prime zeta function and Bessel's inequality are his primary areas of study.
Many of his research projects under Pure mathematics are closely connected to Vinogradov with Vinogradov, tying the diverse disciplines of science together.
Hugh L. Montgomery has included themes like Extreme value theory and Mathematical physics in his Riemann zeta function study.
His Prime zeta function research incorporates elements of Discrete mathematics, Conjugacy class and Prime, Prime ideal.
Multiplicative number theory is closely connected to Prime number in his research, which is encompassed under the umbrella topic of Large sieve.
His study looks at the intersection of Multiplicative number theory and topics like Probabilistic number theory with Multiplicative function.
His most cited work include:
- Topics in Multiplicative Number Theory (594 citations)
- Ten lectures on the interface between analytic number theory and harmonic analysis (549 citations)
- Multiplicative Number Theory I: Classical Theory (489 citations)
What are the main themes of his work throughout his whole career to date?
Hugh L. Montgomery focuses on Pure mathematics, Mathematical analysis, Multiplicative number theory, Discrete mathematics and Riemann zeta function.
His Pure mathematics research incorporates themes from Statistics and Exponential function.
Hugh L. Montgomery has researched Multiplicative number theory in several fields, including Multiplicative function, Prime number theorem and Number theory.
His research in Discrete mathematics intersects with topics in Prime power, Prime, Random variable and Field.
His Riemann zeta function research includes themes of Riemann hypothesis, Combinatorics and Mathematical physics.
The various areas that Hugh L. Montgomery examines in his Combinatorics study include Function and Distribution.
He most often published in these fields:
- Pure mathematics (31.91%)
- Mathematical analysis (29.79%)
- Multiplicative number theory (24.47%)
What were the highlights of his more recent work (between 2004-2018)?
- Multiplicative number theory (24.47%)
- Pure mathematics (31.91%)
- Algebra (19.15%)
In recent papers he was focusing on the following fields of study:
His primary scientific interests are in Multiplicative number theory, Pure mathematics, Algebra, Mathematical analysis and Number theory.
His research integrates issues of Multiplicative function, Additive function and Discrete mathematics in his study of Multiplicative number theory.
His study involves Riemann zeta function, Riemann hypothesis and Analytic number theory, a branch of Pure mathematics.
His Riemann zeta function study frequently links to adjacent areas such as Mathematical physics.
His study in the fields of Euler's formula under the domain of Mathematical analysis overlaps with other disciplines such as Semi-implicit Euler method.
His research in Number theory tackles topics such as Mathematics education which are related to areas like Natural number.
Between 2004 and 2018, his most popular works were:
- Multiplicative Number Theory I: Classical Theory (489 citations)
- Beurling primes with large oscillation (24 citations)
- Analytic Number Theory (12 citations)
In his most recent research, the most cited papers focused on:
- Algebra
- Mathematical analysis
- Number theory
Hugh L. Montgomery spends much of his time researching Algebra, Multiplicative number theory, Combinatorics, Discrete mathematics and Prime number theorem.
His biological study spans a wide range of topics, including Dirichlet character and Möbius function.
His work on Abstract analytic number theory is typically connected to C-minimal theory as part of general Multiplicative number theory study, connecting several disciplines of science.
His Abstract analytic number theory study combines topics in areas such as Multiplicative function, Natural number, Mathematics education and Probabilistic number theory.
In his work, Analytic number theory is strongly intertwined with Field, which is a subfield of Discrete mathematics.
His Zero research is multidisciplinary, relying on both Riemann zeta function and Pure mathematics.
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