Researcher Database

（Last updated : 2024-11-05 12:46:33）　

MURATA MANABU

Department / Course College of Science and Engineering Department of Electrical and Electronic Engineering

Title / Position Lecturer

Academic background
1.	1995/04/01～1999/03/31	Mathematics and Physics, Math Course │ Science and Engineering │ Ritsumeikan University │ Graduated
2.	1999/04/01～2001/03/31	Doctoral Program (1st Semester) │ Mathematics │ Science and Engineering │ Ritsumeikan University Graduate School │ Completed
3.	2001/04/01～2004/03/31	Doctoral Program (2nd Semester) │ Mathematical Sciences │ Science and Engineering │ Ritsumeikan University Graduate School │ Accomplished credits for doctoral program
4.	2006/03/10 Degree Acquisition	Doctor of Science (Mathematics)

Business career
1.	2006/04/01 ～ 2007/03/31	Assistant │ Science and Engineering │ Ritsumeikan University
2.	2007/04/01 ～ 2024/03/31	Part-time Lecturer │ Science and Engineering │ Ritsumeikan University
3.	2024/04/01 ～	Lecturer │ Science and Engineering │ Ritsumeikan University

Subject of research
1.	Arithmetic of quadratic forms

Research summary
There is an ancient problem in mathematics: to study the integral representations of an integer by a quadratic form. Many mathematicians, Fermat, Lagrange, and Gauss for example, discussed this problem. Professor Shimura studied in 2004 the orbits of such representations on a lattice under the stabilizer of the lattice in the orthogonal group. I am interested in the "primitive integral representations" of an integer (or a quadratic form) by a quadratic form, which is closely connected with his theory. As one of the main results, I gave an explicit formula for the number of primitive representations of an integer by a definite quadratic form in 4 variables.

Present specialized field
Algebra /Number theory (Keyword：Quadratic forms)

Papers
1.	2006	Shimura's mass formula for an orthogonal group over real quadratic fields │ Acta Arithmetica │ 121 (2),pp.125-148 (Sole-authored)
2.	2007	On the applications of Shimura’s mass formula │ Proceedings of the Symposium on Algebraic Number Theory and Related Topics, RIMS Kokyuroku Bessatsu │ B4,pp.51-61 (Sole-authored)
3.	2013	On primitive solutions of quadratic Diophantine equation with four variables │ Journal of Number Theory │ 133 (7),pp.2431-2454 (Sole-authored)
4.	2014	On quadratic Diophantine equations in four variables and orders associated with lattices │ Documenta Mathematica │ 19,pp.247-284 (Sole-authored)
5.	2015	On quadratic Diophantine equations in four variables and orders associated with lattices II │ Journal of Number Theory │ 149 (4),pp.166-200 (Sole-authored)
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Academic conference presentation
1.	2006/08	Shimura mass formula over real quadratic fields (Summer school in Sapporo)
2.	2006/12	On the applications of Shimura’s mass formula (Algebraic number theory and related topics)
3.	2014/08	On quadratic Diophantine equations in four variables (ICM 2014 Satellite Conference on Integral Quadratic Forms and Related Topics)
4.	2015/07	On primitive representations of an integer by a quaternary quadratic form (Seminar in number theory and automorphic forms)