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Suzuki Lab
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An analytic number theory lab that studies zeta functions and L-functions using methods from analysis.
AboutAbout the lab
Examining zeta functions through the lens of analysis
Suzuki Lab studies analytic number theory, the branch of number theory that investigates the properties of zeta functions and L-functions.
Besides classical zeta functions, the lab also studies zeta functions of arithmetic schemes and algebraic groups.
The lab also works on the connections between zeta functions and other fields, such as arithmetic geometry, representation theory, functional analysis, and partial differential equations.
Master's theses supervised in the lab cover a variety of topics, including the distribution of prime numbers, integer partitions, and zeros of zeta functions.
Key terms
- Analytic number theory
- A branch of number theory that uses methods of analysis, such as differentiation and integration, to study properties of integers, such as the distribution of prime numbers.
- Zeta function
- A special function that reflects information about prime numbers and integers. A typical example is the Riemann zeta function.
- L-function
- A generalization of the zeta function, constructed for each of the various objects that appear in number theory.
ResearchResearch themes
*Illustrative imageThe "Screw Function" of Zeta Functions
The lab studies a function called the "screw function" that corresponds to the Riemann zeta function, which holds the mysteries of the distribution of prime numbers. Using its properties, the lab approaches the locations of the zeros of zeta functions and the Goldbach problem of expressing an even number as the sum of two primes.
The Riemann Hypothesis and Probability Distributions
The Riemann Hypothesis, one of the greatest unsolved problems in mathematics, can sometimes be restated in the language of probability theory. The lab investigates the "infinitely divisible" probability distributions linked to the hypothesis, exploring new connections between number theory and probability theory.
MembersFaculty
- ProfessorMasatoshi SuzukiPublications ↗
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Complex zeta” Jan Homann / Public domain (cropped)
- The "Screw Function" of Zeta Functions: “Goldbach 3” Fournier Paul / CC0 (cropped)
- Related lab (プルカイト研究室): “J-inv-phase” Linas Vepstas / CC BY-SA 3.0 (cropped)
- Related lab
(利根川研究室): “Minimalfläche mit Seifenhaut Würfel 0328” Bin im Garten / CC BY-SA 3.0 (cropped) - Related lab (田口研究室): “Ulam spiral with prime numbers and divisor-based dot sizes” Marianoju / CC BY-SA 4.0 (cropped)
- Related lab (谷田川研究室): “Riemann surface sqrt” Jan Homann / Public domain (cropped)
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