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Shinichi Kobayashi Last modified date：2024.04.05

Professor / Division of Algebra and Geometry
Faculty of Mathematics




Homepage
https://kyushu-u.elsevierpure.com/en/persons/shinichi-kobayashi
　Reseacher Profiling Tool　Kyushu University Pure
https://sites.google.com/view/shinichikobayashi
Academic Degree
Mathematical Sciences
Country of degree conferring institution (Overseas)
No
Field of Specialization
Number Theory
Total Priod of education and research career in the foreign country
04years00months
Research
Research Interests
  • Iwasawa theory for elliptic curves and modular forms
    keyword : Iwasawa theory, elliptic curves, modular forms
    2002.10～2016.12.
Academic Activities
Papers
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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. 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..
3. Kazuto Ota, Shinichi Kobayashi, Anticyclotomic main conjecture for modular forms and integral Perrin-Riou twists, Proceedings of Iwasawa 2017, 2019.12.
4. 小林 真一, The local root number of elliptic curves with wild ramification, Mathematische Annalen, 323, 3, 609-623, 2002.10.
5. 小林 真一, Iwasawa theory for elliptic curves at supersingular primes, Inventiones mathematicae, 152, 3, 609-623, 2003.10.
6. 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.
Presentations
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Awards
  • Iwasawa theory for elliptic curves at supersingular primes


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