Yasutaka Ihara (伊原康隆, ''Ihara Yasutaka''; born 1938,

Tokyo Prefecture Tokyo, officially the Tokyo Metropolis, is the capital and most populous city in Japan. With a population of over 14 million in the city proper in 2023, it is one of the most populous urban areas in the world. The Greater Tokyo Area, which ...

) is a Japanese

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and professor emeritus at the

Research Institute for Mathematical Sciences The is a research institute attached to Kyoto University, hosting researchers in the mathematical sciences from all over Japan. RIMS was founded in April 1963. List of directors * Masuo Fukuhara (1963.5.1 – 1969.3.31) * Kōsaku Yosida (1969 ...

. His work in number theory includes Ihara's lemma and the

Ihara zeta function In mathematics, the Ihara zeta function is a zeta function associated with a finite graph. It closely resembles the Selberg zeta function, and is used to relate closed walks to the spectrum of the adjacency matrix. The Ihara zeta function was first ...

Career

Ihara received his PhD at the

University of Tokyo The University of Tokyo (, abbreviated as in Japanese and UTokyo in English) is a public research university in Bunkyō, Tokyo, Japan. Founded in 1877 as the nation's first modern university by the merger of several pre-westernisation era ins ...

in 1967 with thesis ''Hecke polynomials as congruence zeta functions in elliptic modular case''. From 1965 to 1966, Ihara worked at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

. He was a professor at the University of Tokyo and then at the Research Institute for Mathematical Science (RIMS) of the University of Kyōto. In 2002 he retired from RIMS as professor emeritus and then became a professor at

Chūō University , commonly referred to as or , is a private research university in Hachioji, Tokyo, Japan. The university finds its roots in a school called Igirisu Hōritsu Gakkō (English Law School), which was founded in 1885, and became a university in 1 ...

. In 1970, he was an invited speaker (with lecture ''Non abelian class fields over function fields in special cases'') at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

(ICM) in

Nice Nice ( ; ) is a city in and the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly one million Kyōto Kyoto ( or ; Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in the Kansai region of Japan's largest and most populous island of Honshu. , the city had a population of 1.46 million, making it the ninth-most pop ...

. His doctoral students include Kazuya Katō.

Research

Ihara has worked on geometric and number theoretic applications of

Galois theory In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field (mathematics), field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems ...

. In the 1960s, he introduced the eponymous Ihara zeta function. In

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

the Ihara zeta function has an interpretation, which was conjectured by

Jean-Pierre Serre Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inau ...

and proved by

Toshikazu Sunada is a Japanese mathematician and author of many books and essays on mathematics and mathematical sciences. He is professor emeritus of both Meiji University and Tohoku University. He is also distinguished professor of emeritus at Meiji in recogni ...

in 1985. Sunada also proved that a

regular graph In graph theory, a regular graph is a Graph (discrete mathematics), graph where each Vertex (graph theory), vertex has the same number of neighbors; i.e. every vertex has the same Degree (graph theory), degree or valency. A regular directed graph ...

is a

Ramanujan graph In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are excellent expander graph, spectral expanders. As Murty's survey ...

if and only if its Ihara zeta function satisfies an analogue of the

Riemann hypothesis In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in pure ...

. See p.678

Selected works

* On Congruence Monodromy Problems, Mathematical Society of Japan Memoirs, World Scientific 2009 (based on lectures in 1968/1969) * with Michael Fried (ed.): Arithmetic fundamental groups and noncommutative Algebra, American Mathematical Society, Proc. Symposium Pure Math. vol.70, 2002 * as editor: Galois representations and arithmetic algebraic geometry, North Holland 1987 * with Kenneth Ribet,

(eds.): Galois Groups over Q, Springer 1989 (Proceedings of a Workshop 1987)

References

External links

Yasutaka Ihara's homepage at RIMS

The Ihara Zeta Function and the Riemann Zeta Function by Mollie Stein, Amelia Wallace
Living people 20th-century Japanese mathematicians 21st-century Japanese mathematicians 1938 births Number theorists University of Tokyo alumni Academic staff of the University of Tokyo Scientists from Tokyo Metropolis {{mathematician-stub