修論タイトル: Relative power integral bases in ray class fields of an imaginary quadratic number field
概要：Schertzは幾つかの例外を除いて「虚二次体上の射類体は相対冪整基底をもつ(整数環が一元生成である)」こと示していた。この例外に関して以下を示した。
R. Sekigawa, Relative power integral bases in certain ray class fields of an imaginary quadratic number field, preprint
吉﨑彪雅 (D1)
研究課題: Weber's Class Number Problem, Unit Groups, Continued Fractions.
修論タイトル: Continued Fraction Expansion and Explicit Minkowski Unit for Weber's Class Number Problem
概要：「Q上のZ2拡大において、全ての中間体の類数が1になる」という"ウィーバーの類数問題"に取り組んだ。相対単数群やPell方程式の理論を用いて、総実体上の具体的な連分数展開に関する予想を定式化し、部分的な結果を得た。
内田直希 (2019年度卒業)
修論タイトル: Integers represented by positive definite binary quadratic forms
概要：正定値2次形式で表される自然数に関する研究。特に「自然数が導手や判別式と互いに素とは限らない場合」に新規性のある結果を得た。"相対導手"という概念を定義・研究し、虚二次体の整環におけるイデアルの分解法則が考察されている。
論文:
N. Uchida, Integers of the Form ax^2 +bxy+cy^2, Eur. J. Math.
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
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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
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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
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On Yoshida's conjecture concerning CM-periods and multiple gamma functions, 21st Autumn Workshop on Number Theory (Hakuba), 2018/9/17
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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
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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
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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
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On a refinement of the reciprocity law on Stark units, Colloquium (Kyoto univ.), 2017/5/31
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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
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Stark-Tateの定式化, Number Theory Summer School ``the Stark conjecture'' (Aso, Kumamoto), 2012/9/2
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有理数体上のStark予想の証明, Number Theory Summer School ``the Stark conjecture'' (Aso, Kumamoto), 2012/9/2
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Frobenius actions on Fermat curves and cyclotomic units, Symposium on Arithmetic & Geometry (Kyushu univ.), 2012/6/2
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
