| 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, https://doi.org/10.1017/S147474802300021X, 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, https://doi.org/10.4007/annals.2021.194.3.8, 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. |
