|
Hiroshi Saito (mathematician)
was a Japanese mathematician at the Research Institute for Mathematical Sciences who worked on automorphic forms. He introduced the and the Saito–Kurokawa lift In mathematics, the Saito–Kurokawa lift (or lifting) takes elliptic modular forms to Siegel modular forms of degree 2. The existence of this lifting was conjectured in 1977 independently by Hiroshi Saito and . Its existence was almost proved by , ... .
Referen ...
|
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 (1969.4.1 – 1972.3.31) * Hisaaki Yoshizawa (1972.4.1 – 1976.3.31) * Kiyoshi Itō (1976.4.1 – 1979.4.1) * Nobuo Shimada (1979.4.2 – 1983.4.1) * Heisuke Hironaka (1983.4.2 – 1985.1.30) * Nobuo Shimada (1985.1.31 – 1987.1.30) * Mikio Sato (1987.1.31 – 1991.1.30) * Satoru Takasu (1991.1.31 – 1993.1.30) * Huzihiro Araki (1993.1.31 – 1996.3.31) * Kyōji Saitō (1996.4.1 – 1998.3.31) * Masatake Mori (1998.4.1 – 2001.3.31) * Masaki Kashiwara (2001.4.1 – 2003.3.31) * Yōichirō Takahashi (2003.4.1 – 2007.3.31) * Masaki Kashiwara (2007.4.1 – 2009.3.31) * Shigeru Morishige (2009.4.1 – 2011.3.31) * Shigefumi Mori (2011.4.1 – 2014.3.31) * Shigeru Mukai (2014.4.1 – 2017.3.31) * Michio Yamada (2017.4.1 – present) Not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automorphic Form
In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular forms are holomorphic automorphic forms defined over the groups SL(2, R) or PSL(2, R) with the discrete subgroup being the modular group, or one of its congruence subgroups; in this sense the theory of automorphic forms is an extension of the theory of modular forms. More generally, one can use the adelic approach as a way of dealing with the whole family of congruence subgroups at once. From this point of view, an automorphic form over the group ''G''(A''F''), for an algebraic group ''G'' and an algebraic number field ''F'', is a complex-valued function on ''G''(A''F'') that is left ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base Change Lifting
In mathematics, base change lifting is a method of constructing new automorphic forms from old ones, that corresponds in Langlands philosophy to the operation of restricting a representation of a Galois group to a subgroup. The Doi–Naganuma lifting from 1967 was a precursor of the base change lifting. Base change lifting was introduced by for Hilbert modular form In mathematics, a Hilbert modular form is a generalization of modular forms to functions of two or more variables. It is a (complex) analytic function on the ''m''-fold product of upper half-planes \mathcal satisfying a certain kind of functional e ...s of cyclic totally real fields of prime degree, by comparing the trace of twisted Hecke operators on Hilbert modular forms with the trace of Hecke operators on ordinary modular forms. gave a representation theoretic interpretation of Saito's results and used this to generalize them. extended the base change lifting to more general automorphic forms and showed how to u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saito–Kurokawa Lift
In mathematics, the Saito–Kurokawa lift (or lifting) takes elliptic modular forms to Siegel modular forms of degree 2. The existence of this lifting was conjectured in 1977 independently by Hiroshi Saito and . Its existence was almost proved by , and and completed the proof. Statement The Saito–Kurokawa lift ''σ''''k'' takes level 1 modular forms ''f'' of weight 2''k'' − 2 to level 1 Siegel modular forms of degree 2 and weight ''k''. The L-functions (when ''f'' is a Hecke eigenforms) are related by ''L''(''s'',''σ''''k''(''f'')) = ζ(''s'' − ''k'' + 2)ζ(''s'' − ''k'' + 1)''L''(''s'', ''f''). The Saito–Kurokawa lift can be constructed as the composition of the following three mappings: # The Shimura correspondence from level 1 modular forms of weight 2''k'' − 2 to a space of level 4 modular forms of weight ''k'' − 1/2 in the Kohnen plus-space. #A map from the Kohnen plus-space t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2010 Deaths
This is a list of deaths of notable people, organised by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked here. 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 See also * Lists of deaths by day The following pages, corresponding to the Gregorian calendar, list the historical events, births, deaths, and holidays and observances of the specified day of the year: Footnotes See also * Leap year * List of calendars * List of non-standard ... * Deaths by year {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
