Kyushu University Academic Staff Educational and Research Activities Database
List of Papers
Shinichi Kobayashi Last modified date:2024.04.05

Professor / Division of Algebra and Geometry / Faculty of Mathematics

1. Ashay Burungale, Shinichi Kobayashi, Kazuto Ota, p-adic L-functions and rational points on CM elliptic curves at inert primes, Journal of the Institute of Mathematics of Jussieu,, 2023.07, Let K be an imaginary quadratic field and p≥5 a rational prime inert in K. For a Q-curve E with complex multiplication by OK and good reduction at p, K. Rubin introduced a p-adic L-function L_E which interpolates special values of L-functions of E twisted by anticyclotomic characters of K. In this paper, we prove a formula that links certain values of L_E outside its defining range of interpolation with rational points on E. Arithmetic consequences include p-converse to the Gross–Zagier and Kolyvagin theorem for E..
2. Shinichi Kobayashi, A p-adic interpolation of generalized Heegner cycles and integral Perrin-Riou twist I, Annales mathematiques du Quebec, 10.1007/s40316-023-00213-4, 47, 73-116, 2023.03.
3. Ashay A. Burungale, Shinichi Kobayashi, Kazuto Ota, Rubin’s conjecture on local units in the anticyclotomic tower at inert primes, Annals of Mathematics,, 194, 3, 2021.11, 惰性的素数におけるCM楕円曲線の反円分岩澤理論における基本的はRubin予想を解決した..
4. Kazuto Ota, Shinichi Kobayashi, Anticyclotomic main conjecture for modular forms and integral Perrin-Riou twists, Proceedings of Iwasawa 2017, 2019.12.
5. Kenichi Bannai, Shinichi Kobayashi, Seidai Yasuda, The radius of convergence of the p-adic sigma function., Mathematische Zeitschrift , 286, 1-2, 751-781, 2017.01.
6. 小林 真一, The local root number of elliptic curves with wild ramification, Mathematische Annalen, 323, 3, 609-623, 2002.10.
7. 小林 真一, Iwasawa theory for elliptic curves at supersingular primes, Inventiones mathematicae, 152, 3, 609-623, 2003.10.
8. 小林 真一, An Elementary Proof of the Mazur-Tate-Teitelbaum Conjecture for Elliptic Curves, Documenta mathematica, Extra Volume, John H. Coates' Sixtieth Birthday, 567-575, 2006.10.
9. 小林 真一, 坂内健一, Algebraic theta functions and p-adic interpolation of Eisenstein-Kronecker numbers, Duke Mathematical Journal, 153, 2, 229-295, 2010.10.
10. 小林 真一, 山崎隆雄, Torsion points on Jacobian varieties via Anderson's p-adic Soliton Theory, Asian Journal of mathematics , 20, 2, 323-352, 2016.01.
11. 小林 真一, 坂内健一, Integral structures on p-adic Fourier theory, Annales de L'Institut Fourier, 66, 1, 521-550, 2016.01.