What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Algebra
- Complex number
His primary areas of investigation include Ramanujan's sum, Pure mathematics, Combinatorics, Ramanujan theta function and Algebra.
His research in Ramanujan's congruences, Ramanujan tau function, Rogers–Ramanujan identities, Ramanujan prime and Rogers–Ramanujan continued fraction are components of Ramanujan's sum.
His study looks at the relationship between Ramanujan tau function and fields such as Eisenstein series, as well as how they intersect with chemical problems.
His work carried out in the field of Ramanujan prime brings together such families of science as Triangular number and Ramanujan summation.
His work on Gauss sum and Cusp form is typically connected to Quadratic reciprocity and Quadratic Gauss sum as part of general Pure mathematics study, connecting several disciplines of science.
Chowla–Selberg formula, Arithmetic function, Order, Sign and Bessel function is closely connected to Dirichlet series in his research, which is encompassed under the umbrella topic of Combinatorics.
His most cited work include:
- Ramanujan’s Notebooks: Part V (1510 citations)
- Gauss and Jacobi sums (571 citations)
- Ramanujan's Notebooks (565 citations)
What are the main themes of his work throughout his whole career to date?
Bruce C. Berndt mainly investigates Ramanujan's sum, Pure mathematics, Combinatorics, Algebra and Ramanujan theta function.
His research brings together the fields of Series and Ramanujan's sum.
His work in the fields of Pure mathematics, such as Eisenstein series, Theta function and Modular form, overlaps with other areas such as Modular equation.
His Combinatorics research is multidisciplinary, relying on both Fraction and Dirichlet series.
In his works, Bruce C. Berndt undertakes multidisciplinary study on Ramanujan theta function and j-invariant.
The various areas that Bruce C. Berndt examines in his Ramanujan tau function study include Discrete mathematics and Euler function.
He most often published in these fields:
- Ramanujan's sum (64.45%)
- Pure mathematics (39.13%)
- Combinatorics (26.60%)
What were the highlights of his more recent work (between 2010-2021)?
- Ramanujan's sum (64.45%)
- Combinatorics (26.60%)
- Pure mathematics (39.13%)
In recent papers he was focusing on the following fields of study:
His primary scientific interests are in Ramanujan's sum, Combinatorics, Pure mathematics, Algebra and Series.
His study in Ramanujan theta function and Ramanujan tau function are all subfields of Ramanujan's sum.
His research in Ramanujan theta function intersects with topics in Third order and Order.
His Combinatorics research incorporates elements of Eisenstein series and Dirichlet series.
His studies in Pure mathematics integrate themes in fields like Elliptic function and Trigonometric integral.
Bruce C. Berndt has included themes like Divisor, Fraction and Bessel function in his Series study.
Between 2010 and 2021, his most popular works were:
- Asymptotic expansions of certain partial theta functions (46 citations)
- Circle and divisor problems, and double series of Bessel functions (21 citations)
- Weighted divisor sums and Bessel function series, II (20 citations)
In his most recent research, the most cited papers focused on:
- Algebra
- Mathematical analysis
- Complex number
Ramanujan's sum, Combinatorics, Pure mathematics, Algebra and Bessel function are his primary areas of study.
His Ramanujan's sum research is multidisciplinary, incorporating perspectives in Discrete mathematics, Number theory, Theta function, Eisenstein series and Dirichlet series.
Ramanujan tau function and Modular form are subfields of Pure mathematics in which his conducts study.
His research in Ramanujan tau function is mostly concerned with Ramanujan summation.
His work in the fields of Algebra, such as Rogers–Ramanujan identities and Rogers–Ramanujan continued fraction, intersects with other areas such as j-invariant and Elliptic rational functions.
His Bessel function research incorporates themes from Transformation and Series.
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