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Narita Lab
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A number theory lab that investigates the properties of integers and prime numbers using automorphic forms, a type of function.
AboutAbout the lab
Approaching the properties of integers through automorphic forms
The Narita Lab studies number theory, in particular functions called automorphic forms.
Number theory is a field of mathematics that investigates the properties of prime numbers and integer solutions, and automorphic forms are one of its research tools.
The lab works on constructing automorphic forms explicitly and clarifying their number-theoretic properties.
Key terms
- Number theory
- A field of mathematics that investigates the properties of integers themselves, such as prime numbers and integer solutions
- Automorphic form
- A special function with symmetry, used as a tool for investigating number theory
- L-function
- A function expressed as an infinite series (an infinite sum), used to investigate the properties of integers
ResearchResearch themes
Within number theory, the lab studies functions with symmetry called automorphic forms. It aims to construct automorphic forms explicitly and clarify their number-theoretic properties.
*Illustrative imageNon-holomorphic Automorphic Forms
The lab works on explicitly constructing automorphic forms on symmetric spaces, such as quaternionic hyperbolic space, that do not fit within complex symmetric domains.
*Illustrative imageConstructing Counterexamples to the Ramanujan Conjecture
The lab is working on explicitly constructing real-analytic automorphic forms on orthogonal groups of rank 1 that serve as counterexamples to the Ramanujan conjecture.
MembersFaculty
- Hiroaki Narita
VoicesStudent voices
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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: “Beeswax foundation” Plantsurfer / Public domain (cropped)
- Non-holomorphic Automorphic Forms: “Hyperbolic plane” Durova / CC BY-SA 3.0 (cropped)
- Constructing Counterexamples to the Ramanujan Conjecture: “Black swan (Cygnus atratus) Bruny” Charles J. Sharp / CC BY-SA 4.0 (cropped)
- Related lab (尾﨑研究室): “Minoritenkirche rose window - Vienna” MrPanyGoff / CC BY-SA 3.0 (cropped)
- Related lab (池田研究室): “Mathematisches-Gipsmodell.Fläche3.Ordnung - Kopie” Museopedia / CC BY-SA 4.0 (cropped)
- Related lab (薄葉研究室): “CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique” Jérémy Barande / CC BY-SA 3.0 (cropped)
- Related lab (小川研究室): “Chladni plate 14” Exhibit made by Estes Objethos Atelier, photo by Rodrigo Tetsuo Argenton / CC BY-SA 4.0 (cropped)
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