Japanese

Hello. My name is Tomokazu Kashio.
I am studying Number Theory.



My hobby is (was) ultimate Frisbee. I believe that I was a pretty good player!


Profile

---

list of papers

• Y. Hirakawa, T. KASHIO, R. Sekigawa, N. Takada, S. Yamamoto, A note on the second supplementary law of rational power residue symbols, preprint (arXiv:2504.11666)
• T. Kashio, H. Yoshizaki, Minimal relative units of the cyclotomic Z_2-extension, preprint (arXiv:2107.08587)
• T. Kashio, On a common refinement of Stark units and Gross-Stark units, to appear in Journal of the London Mathematical Society (arXiv:1706.03198)
• T. Kashio, Note on Coleman's formula for the absolute Frobenius on Fermat curves, Annales de l'Institut Fourier 74 (2024), no. 3, 1229-1250
• T. Kashio, R. Sekigawa, The characterization of cyclic cubic fields with power integral bases, Kodai Math. J. 44(2) (2021), 290-306
• T. Kashio, A period-ring-valued gamma function and a refinement of the reciprocity law on Stark units, RIMS Kokyuroku Bessatsu B83 (2020), 169-181
• T. Kashio, p-adic measures associated with zeta values and p-adic log multiple gamma functions, Int. J. Number Theory 15 (2019), no. 5, 991--1007
• T. Kashio, On the ratios of Barnes' multiple gamma functions to the p-adic analogues. J. Number Theory 199 (2019), 403-435
• T. Kashio, Fermat curves and a refinement of the reciprocity law on cyclotomic units. J. Reine Angew. Math. 741 (2018), 255-273
• T. Kashio, On the algebraicity of some products of special values of Barnes' multiple gamma function. Amer. J. Math. 140 (2018), no. 3, 617-651
• T. Kashio, Stark's conjecture over the rational number field and CM-periods of Fermat curves, RIMS Kokyuroku Bessatsu, B64 (2017), 93-106
• T. Kashio, A survey on Stark's conjectures and a result of Dasgupta-Darmon-Pollack, RIMS Kokyuroku Bessatsu, B51 (2014), 229-268
• T. Kashio, Stark's units, CM-periods and multiple gamma functions, Surikaisekikenkyusho Kokyuroku No. 1659 (2009), 82-95
• T. Kashio, H. Yoshida, On p-adic absolute CM-periods. II. Publ. Res. Inst. Math. Sci. 45 (2009), no. 1, 187-225
• T. Kashio, H. Yoshida, On p-adic absolute CM-periods. I. Amer. J. Math. 130 (2008), no. 6, 1629-1685
• T. Kashio, H. Yoshida, On the p-adic absolute CM-period symbol. Algebra and number theory, Hindustan Book Agency, Delhi (2005), 359-399
• T. Kashio, On a p-adic analogue of Shintani's formula. J. Math. Kyoto Univ. 45 (2005), no. 1, 99-128
• T. Kashio, H. Yoshida, p-adic absolute CM-Periods I,II, Proceedings of the 8th Autumn Workshop on Number Theory at Hakuba (2005), 60-88
• T. Kashio, H. Yoshida, On p-adic absolute CM-Periods, Proceedings of the 7th Autumn Workshop on Number Theory at Hakuba (2005), 161-176

list of papers in Japanese

• 加塩朋和, ガンマ関数の関数等式とCM周期の単項関係式の対応とその応用, 第67回代数学シンポジウム報告集 (2023), 73-84
• 加塩朋和, On a common refinement of Stark units and Gross-Stark units, 早稲田大学整数論研究集会 2019報告集 (2021), 1-11
• 加塩朋和, Stark-Tateの定式化, 有理数体上のStark予想の証明, Rubin's integral refinement, 第20回整数論サマースクール「Stark予想」報告集 (2013), 1-14, 15-26, 93-104
• 加塩朋和, On a relation between p-adic multiple gamma functions and p-adic periods, RIMS Kokyuroku Bessatsu B25 (2011), 31-51
• 加塩朋和, Kronecker limit formulaと関連する話題, Heegner pointとGross-Zagier公式の勉強会報告集 (2010), 339-349
• 加塩朋和, Skinner-Wiles の底変換(base change) 議論, 報告集「R=Tの最近の発展 佐藤・Tate予想とSerre予想」(2009), 359-379
• 加塩朋和, 新谷公式のp進類似とその応用, 早稲田大学整数論研究集会2007報告集 (2007), 118-124
• 加塩朋和, 吉田敬之, p進多重ガンマ関数を用いた類体構成, Surikaisekikenkyusho Kokyuroku No. 1521 (2006), 86-98
• 加塩朋和, 吉田敬之, On the p-adic absolute CM-Period symbol, Surikaisekikenkyusho Kokyuroku No. 1451 (2005), 9-18
• 加塩朋和, p-adic analogue of Shintani's formula, Surikaisekikenkyusho Kokyuroku No. 1324 (2003), 47-57

list of talks

• 冪乗剰余の第二補充法則に関して, プロジェクト研究集会2024 (静岡県伊豆の国市), 2025/3/19
  -> slides (in Japanese)
• On periods and the absolute Frobenius on Fermat curves, L-functions and Motives in Niseko2024 (北海道ニセコ町), 2024/9/19
  -> slides
• 円分Z2拡大の極小相対単数について, プロジェクト研究集会2023 (静岡県熱海市), 2024/3/11
  
• フェルマー曲線上のフロベニウス行列の公式とその一般化に関して, プロジェクト研究集会2022 (長野県佐久市), 2023/3/21
  -> resume (in Japanese)
• "ガンマ関数の関数等式"と"CM周期の単項関係式"の対応と、その応用, 第67回代数学シンポジウム, (RIMS), 2022/8/31
  -> slides (in Japanese)
• p進ガンマ関数の関数等式と連続性に関して, プロジェクト研究集会2021 (慶応義塾大学, online), 2022/3/17
  -> slides (in Japanese)
• 整数論(の極一部)におけるｐ進的手法の紹介, 代数学の萌芽 (東京理科大学野田キャンパス), 2022/3/4
  -> slides (in Japanese)
• CM周期，多重ガンマ関数，Stark予想の関係とそのp進類似, Dasgupta Kakde Workshop (慶應義塾大学矢上キャンパス), 2022/2/18
  -> slides (in Japanese)
• A note on the monogenity and the unit group, Second meeting of Monogenity and power integral bases (Debrecen, online), 2021/3/11
  -> slides
• CM周期の代数的整数論への応用の紹介, プロジェクト研究集会2020 (慶応義塾大学, online), 2021/3/11
  -> slides (in Japanese)
• 円単数の相互法則の細分, 及びその一般化, 第18回北陸数論研究集会「数論における相互法則」(金沢大学サテライトプラザ), 2019/12/26
  -> resume (in Japanese)
• フェルマー曲線上の絶対フロベニウスに関するコールマンの公式について, 2019大分佐賀整数論研究集会(佐賀大学), 2019/10/13
  -> slides (in Japanese)
• On Coleman's formula for the absolute Frobenius on Fermat curves, 愛知数論セミナー(愛知工業大学), 2019/3/30
  -> resume (in Japanese)
• On a common refinement of Stark units and Gross-Stark units, 2019早稲田整数論研究集会, 2019/3/13
  -> resume (in Japanese)
• 類体構成の具体例, 及び p 進周期との関係について, 坂内研究室プロジェクト研究集会 (静岡県熱海市), 2019/3/6
  -> slides (in Japanese)
• On Yoshida's conjecture concerning CM-periods and multiple gamma functions, 21st Autumn Workshop on Number Theory (Hakuba), 2018/9/17
  -> resume (in English)
• A note on special values of the gamma function, 坂内研究室プロジェクト研究集会 (神奈川県足柄下郡箱根町), 2018/2/27
  -> slides (in Japanese)
• A period-ring-valued gamma function and a refinement of the reciprocity law on Stark units, Algebraic Number Theory and Related Topics (RIMS), 2017/12/6
  -> resume (in English)
• On a relation between CM periods Stark units and multiple gamma functions, Workshop ``Special values of automorphic L-functions periods of automorphic forms and related topics'' (Osaka city univ.), 2017/9/19
  -> slides (in English)
• On a refinement of the reciprocity law on Stark units, Colloquium (Kyoto univ.), 2017/5/31
  -> slides (in Japanese)
• 多重ガンマ関数, 集中講義 数学特別講義 数論II (京都大学数学教室), 2017/5/29--6/2
  -> resume (in Japanese)
• 多重ガンマ関数の単項関係式とその応用, 坂内研究室プロジェクト研究集会 (伊東市), 2017/3/15
  -> slides (in Japanese)
• 有理数体上のStark予想とFermat曲線のCM周期, 神楽坂代数セミナー, 2015/5/22
• Stark's conjecture over the rational number field and CM-periods of Fermat curves, Algebraic Number Theory and Related Topics (RIMS), 2014/12/4
• A product of special values of multiple gamma functions, Japan-Taiwan Joint Conference on Number Theory (Kesennuma, Miyagi), 2014/9/4
• 有理数体上のStark予想の部分的な別証明, Number Theory Seminar at Waseda University, 2013/10/18
• On Shimura's CM-periods and Stark's units over totally real fields, Automorphic Functions and Arithmetic Geometry: a symposium for Prof. L. Lafforgue's visit (Kyushu univ.), 2013/4/26
• CM周期に関する吉田予想とそのp進類似について, Seminar on Arithmetic Algebraic Geometry (Hokkaido univ.), 2012/12/19
• A survey on Stark's conjectures and a result of Dasgupta-Darmon-Pollack, Algebraic Number Theory and Related Topics (RIMS), 2012/12/3
• Rubin's integral refinement, Number Theory Summer School ``the Stark conjecture'' (Aso, Kumamoto), 2012/9/5
  -> proceedings (in Japanese)
• Stark-Tateの定式化, Number Theory Summer School ``the Stark conjecture'' (Aso, Kumamoto), 2012/9/2
  -> proceedings (in Japanese)
• 有理数体上のStark予想の証明, Number Theory Summer School ``the Stark conjecture'' (Aso, Kumamoto), 2012/9/2
  -> proceedings (in Japanese)
• Frobenius actions on Fermat curves and cyclotomic units, Symposium on Arithmetic & Geometry (Kyushu univ.), 2012/6/2
• Stark-Tateの定式化とRubinのintegral refinement, スターク予想に関する小研究会 (金沢大学サテライトプラザ), 2012/3/14
• 有理数体上のスターク予想の別証明, 岩澤理論セミナー (慶応義塾大学), 2011/11/26
• On a relation between p-adic gamma functions and p-adic periods, Workshop on L-Functions (Kyushu univ.), 2011/4/21
• On a relation between p-adic gamma functions and p-adic periods, Mini-workshop on Iwasawa theory (Kyoto univ.), 2011/4/10
• p進ガンマ関数の特殊値とp進周期の関係, 大阪大学整数論・保型形式セミナー, 2010/1/8
• p進多重ガンマ関数とp進周期の関係について, Algebraic Number Theory and Related Topics (RIMS), 2009/12/11
• 対数的p進多重ガンマ関数の定義とその性質, 対数的p 進多重ガンマ関数とp進周期の関係, Workshop ``p-進特殊関数と数論幾何'' (蔵王), 2009/10/30
• On monomial relations of Barnes's multiple gamma function, 8th Hiroshima Workshop on Number Theory, 2009/7/21
• 多重ガンマ関数の満たす単項関係式と関連する話題, Colloquiums of Mathematics at Okayama University, 2009/7/7
• Stark units, CM-periods and multiplegamma functions, UCLA Number Theory Seminar, Los Angeles, 2009/3/6
• Stark units, CM-periods and multiple gamma functions, Workchop ``Automorphic representations automorphic L-functions and arithmetic'' (RIMS), 2009/1/20
• Stark's conjecture, Shintani's methods and Yoshida's class invariants, 11th Autumn Workshop on Number Theory (Hakuba), 2008/9/11
• Periods and the multiple gamma function in the p-adic case, Recent Developments in Number Theory: Selmer Groups L-functions and Galois Deformations (Univ. of California, Los Angeles), 2008/3/27
• On the p-adic absolute CM-period symbol, 2nd Japanese-German Number Theory Workshop (Max Planck Institute for Mathematics, Bonn), 2008/2/22
• Kronecker limit formulaと関連する話題, Heegner pointとGross-Zagier公式の勉強会 (東北大学), 2007/10/12
• p進多重ガンマ関数を用いた類体構成, Algebraic Number Theory and Related Topics (RIMS), 2005/12/6
• p-adic absolute CM-Periods, 8th Autumn Workshop on Number Theory (Hakuba), 2005/9/24
• p-adic absolute CM-periods, Algebraic Number Theory and Related Topics (RIMS), 2004/12/6
• On p-adic absolute CM-Periods, 7th Autumn Workshop on Number Theory (Hakuba), 2004/10/24
• p-adic analogue of Shintani's formula, Algebraic Number Theory and Related Topics (RIMS), 2002/12/3