A CONSTRUCTION OF pp-ADIC ASAI LL-FUNCTIONS OVER CM FIELDS (Analytic, geometric and pp-adic aspects of automorphic forms and LL-functions)

This article is a survey on the author's preprint [Na], where the author constructs a p-adic Asai £-functions for irreducible cohomological cuspidal autmorphic representations of GL₂ over CM fields

A COHOMOLOGICAL INTERPRETATION OF ARCHIMEDEAN ZETA INTEGRALS FOR GL3_{3} timestimes GL2_{2} (Automorphic forms, Automorphic representations, Galois representations, and its related topics)

This article is a survey on the author's preprint [T. Hara and K. Namikawa, A cohomological interpretation of archimedean zeta integrals for GL3 xGL2, preprint, arXiv:2012.13213.], where the author constructs a p-adic Asai L-functions for irreducible cohomological cuspidal autmorphic representations of GL₂ over CM fields

北海道礼文華峠におけるブナ分布北限域孤立個体群の立地と植生

筆者らはブナの分布北限域における最前線孤立個体群を太平洋から水平距離で2.5km内陸に位置する豊浦町礼文華峠の岩峰上及びその周辺で発見した．これはブナの天然分布個体群の中でも太平洋側における最北限の個体群であると考えられた。付近のアメダスのデータによれば，年平均気温7.3 ℃，年降水量1,198 mm，最大積雪深85cmであった．現地の暖かさの指数WIは52.5℃・月と推定された．ブナの分布，植生と立地の状況を明らかにするために現地調査を行った結果，以下の知見を得た．（1）岩峰上に生育する胸高以上のブナは約1.7 haの範囲（標高196 ～ 275 m）に39本生育し，胸高直径階分布は緩やかなL字型を示し，10 cm以下の個体が最多であった．（2） 岩峰のブナは主にミズナラ，ホオノキ，シラカンバと混生し，競合する針葉樹は記録されなかった．（3） 植物群落の種構成は日本海側に成立するブナ林に類似していた．（4） 土壌pHはやや酸性で5.4 ～ 5.5であり，無機態窒素は全国のブナ林の値と大きな違いはなかった．以上の知見から，礼文華峠の岩峰上のブナ個体群は，その生育に適した気候条件に加え，本州の岩峰などでしばしば優占する針葉樹類が不在であるなどの条件が重なって成立したと考えられた

On constructions of theta functions on mathrmGSp4mathrm{GSp}_{4} and its mod pp nonvanishing (Algebraic Number Theory and Related Topics 2012)

"Algebraic Number Theory and Related Topics 2012". December 3～7, 2012. edited by Atsushi Shiho, Tadashi Ochiai and Noriyuki Otsubo. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed

P-adic L-function for GL(n + 1) Ã GL(n) I

A construction of p-adic L-functions for GL(2) via the modular symbol method is reviewed in this talk. I will summarize some technical points of the construction comparing with the works of F. Januszewski on p-adic L-functions for GL(n + 1) Ã GL(n). In particular, the behavior under the Tate twists is emphasized in the talk, since it is the most important new ingredient in Januszewskiâ s recent preprint. Related references (for talks I to IV): (Main) F.Januszewski. Non-abelian p-adic Rankin-Selberg L-functions and non-vanishing of central L- values, arXiv:1708.02616, 2017. K. Namikawa. On p-adic L-functions associated with cusp forms on GL2. manuscr. math. 153, pages 563â 622, 2017. (Sub) B.J. Birch. Elliptic curves over Q, a progress report. 1969 Number Theory Institute. AMS Proc. Symp. Pure Math. XX, 396â 400, 1971. M. Dimitrov. Automorphic symbols, p-adic L-functions and ordinary cohomology of Hilbert modular varieties. Amer. J. Math. 135, 1117â 1155, 2013. F. Januszewski. Modular symbols for reductive groups and p-adic Rankin-Selberg convolutions over number fields, J. Reine Angew. Math. 653, 1â 45, 2011. F. Januszewski. On p-adic L-functions for GL(n)Ã GL(nâ 1) over totally real fields, Int. Math. Res. Not., Vol. 2015, No. 17, 7884â 7949. F. Januszewski. p-adic L-functions for Rankin-Selberg convolutions over number fields, Ann. Math. Quebec 40, special issue in Honor of Glenn Stevens â 60th birthday, 453â 489, 2016. F. Januszewski. On period relations for automorphic L-functions I. To appear in Trans. Amer. Math. Soc., arXiv:1504.06973 H. Kasten and C.-G. Schmidt. On critical values of Rankin-Selberg convolutions. Int. J. Number Theory 9, pages 205â 256, 2013. D. Kazhdan, B. Mazur, and C.-G. Schmidt. Relative modular symbols and Rankin-Selberg convolutions, J. Reine Angew. Math. 512, 97â 141, 2000. K. Kitagawa. On standard p-adic L-functions of families of elliptic cusp forms, p-adic mon- odromy and the Birch and Swinnerton-Dyer conjecture (B. Mazur and G. Stevens, eds.), Con- temp. Math. 165, AMS, 81â 110, 1994. J.I. Manin. Non-archimedean integration and p-adic Hecke-Langlands L-series. Russian Math. Surveys 31, 1, 1976. B. Mazur, and P. Swinnerton-Dyer. Arithmetic of Weil Curves, Invent. Math. 25, 1â 62, 1974. B. Mazur, J. Tate, and J. Teitelbaum. On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Invent. Math. 84, 1â 48, 1986. C.-G. Schmidt. Relative modular symbols and p-adic Rankin-Selberg convolutions, Invent. Math. 112, 31â 76, 1993. C.-G. Schmidt. Period relations and p-adic measures, manuscr. math. 106, 177â 201, 2001. B. Sun. The non-vanishing hypothesis at infinity for Rankin-Selberg convolutions. J. Amer. Math. Soc. 30, pages 1â 25, 2017. A. Raghuram. On the Special Values of certain Rankin-Selberg L-functions and Applications to odd symmetric power L-functions of modular forms. Int. Math. Res. Not. 2010, 334â 372, 2010. A. Raghuram. Critical values for Rankin-Selberg L-functions for GL(n) Ã GL(n â 1) and the symmetric cube L-functions for GL(2). Forum Math. 28, 457â 489, 2016.Non UBCUnreviewedAuthor affiliation: Kyushu UniversityResearche