- 2020 - 2025 擬尖点形式を用いた跡公式の分割と保型形式及びゼータ関数の研究
- 2020 - 2024 代数的保型形式の次元評価
- 2017 - 2020 Study of trace formulas, automorphic forms and zeta functions by using pseudo-cusp forms
- 2015 - 2019 Explicit Fourier transform of trace formulas and its applications to arithmetic
- 2014 - 2017 Resolvent type trace formulas, automorphic forms and zeta functions
- 2011 - 2015 Arithmetic study of automorphic forms of many variables by various method
- 2011 - 2013 Study of automorphic forms and zeta functions by using generalized or refined resolvent type trace formulas
- 2007 - 2010 Resolvent type trace formulas, automorphic forms and number theory
- 2003 - 2005 保型的ポアンカレ級数とレゾルベント型跡公式の整数論
- 2003 - 2005 Research on algorithm to compute special values for non holomorphic Eisenstein series
- 2001 - 2002 離散系列保型形式とセルバーグ跡公式の整数論
- 1998 - 1998 セルバーグ跡公式と保型形式の整数論
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