Noriko HIRATA-Kohno's Home Page

List of Main Publications

The number of published articles: 102

KEY WORDS:
Diophantine approximations, Pade approximations, Polylogarithms, Lerch function, G-function, p-adic polylogarithms,
Linear forms in logarithms, Transcendence, Elliptic logarithms, Subspace Theorem, S-unit equation,
Diophantine equations, Applications of Diophantine problems to cryptosystem.



1. N. Hirata-Kohno, M. Kawashima, A. Poels and Y. Washio, S-unit equation in two variables and Pade approximations
   International Journal of Number Theory, journal page.
2. S. David, N. Hirata-Kohno and M. Kawashima, Generalized hypergeometric G-functions take linear independent values,
   arXiv page.
3. S. David, N. Hirata-Kohno and M. Kawashima, Linear independence criteria for generalized polylogarithms with distinct shifts,
   Acta Arithmetica, 206 (2) 127--169, 2022, journal page.
4. S. David, N. Hirata-Kohno and M. Kawashima, Recent Developments on Polylogarithms and Period Conjecture, RIMS Kokyuroku Bessatsu, in press.
5. S. David, N. Hirata-Kohno and M. Kawashima, Linear forms in polylogarithms,
   Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 23/3, 1447--1490, journal page.
6. S. David, N. Hirata-Kohno and M. Kawashima, Can polylogarithms at algebraic points be linearly independent?
   Moscow J. of Combinatorics and Number Theory, 9, no. 4, 389-406, (2020), journal page.
7. N. Hirata-Kohno, Diophantine Approximation, Exposition, American Mathematical Society, vol. 34, 205--229, journal page.
8. K. Akiyama, S. Nakamura, M. Ito and Noriko Hirata-Kohno, A key exchange protocol relying on polynomial maps,
   International Journal of Mathematics for Industry, vol. 11, (2019), 1950003-1-1950003-11, journal page.
9. H. Furutsu and N. Hirata-Kohno, Linear dependence criterion
   of almost integer valued functions: a generalization of the Polya-Pisot theorem,
   J. Res. Inst. Sci.Tech. Nihon Univ., 144, (2019), 12-16, journal page.
10. N. Hirata-Kohno, M. Ito and Y. Washio, A criterion for the linear independence of polylogarithms over a number field,
    RIMS Kokyuroku Bessatsu, (2017), B. 64, 3--18, journal page.
11. H. Furutsu and N. Hirata-Kohno, Conditions of an Analytic Function to be a Polynomial via Diophantine Approximations,
    Research Institute of Science and Technology, CST, Nihon University (2016), vol. 136, 12--16, journal page.
12. N. Hirata-Kohno and F. Luca, On the Diophantine equation F_n^x+F_{n+1}^x=F_m^y,
    Rocky Mountain Journal of Mathematics, Rocky Mountain Journal of Mathematics (2015), vol. 45, no. 2, 509--538 journal page.
13. N. Hirata-Kohno and T. Kovacs, Computing S-integral points on elliptic curves of rank at least 3,
    RIMS Kokyuroku, Kyoto University, Vol. 1898, (2014), 92--102, journal page.
14. N. Hirata-Kohno, Diophantine approximation related to polylogarithms,
    RIMS Kokyuroku, Kyoto University, Vol. 1898, (2014), 194--206, journal page.
15. A. B\'erczes, L. Hajdu, N. Hirata-Kohno, T. Kovacs and A. Peth\H{o},
    A key exchange protocol based on Diophantine equations and S-integers, JSIAM Letters, vol. 6(2014), 85--88 journal page.
16. N. Hirata-Kohno and A. Peth\H{o}, On a key exchange protocol based on Diophantine equations,
    Infocommunications Journal, ISSN 2061-2079, Vol. 5, (2013), No. 3, 17--21; published pdf (without photo).
17. M. Ito and N. Hirata-Kohno, Optimization for lattices and Diophantine approximations,
    Interdisciplonary Information Sciences, vol. 19, No. 2, (2013), 135--142, journal page.
18. N. Hirata-Kohno, Arithmetic properties of p-adic elliptic polylogarithms and irrationality,
    In: Diophantische Approximationen, Oberwolfach Report Vol. 9, Issue 2, 1347--1351, (2012),
    eds. Y. Bugeaud and Yu. V. Nesterenko, European Math. Society, journal page.
19. N. Hirata-Kohno and H. Okada, A note on linear independence of polylogarithms over the rationals,
    Proceedings of the Japan Academy, series A, 88/9, (2012), 156--161; journal page.
20. N. Hirata-Kohno, Diophantus Approximations, The Mathematical Society of Japan,
    Sugaku, Iwanami, July 2012, vol. 64(3), 254--277, journal page.
21. N. Hirata-Kohno, Arithmetic properties of p-adic elliptic logarithmic functions,
    Series on Number Theory and its Applications, vol. 7, 2011, 110--119.
22. N. Hirata-Kohno and R. Takada, Linear forms in two elliptic logarithms in the p-adic case,
    Kyushu J. of Mathematics, vol. 64, no. 2, (2010), 239--260, journal page.
23. S. David and N. Hirata-Kohno, Linear forms in elliptic logarithms,
    Journal fur die reine und angewandte Mathematik, vol. 628, (2009), 37--89, journal page.
24. N. Hirata-Kohno, S. Laishram, T. N. Shorey and R. Tijdeman, An extension of a theorem of Euler,
    Acta Arithmetica vol. 129 (1), (2007), 71--102, journal page.
25. S. David and N. Hirata-Kohno, Logarithmic Functions and Formal Groups of Elliptic Curves,
    In: Diophantine Equations (ed. N. Saradha), Tata Institute of Fundamental Research, Narosa Publishing House, India, 243--255, book page.
26. S. David and N. Hirata-Kohno, Recent progress on linear forms in elliptic logarithms,
    A Panorama in Number Theory, (ed. G. Wuestholz), Cambridge Univ. Press (2002), 26--37, book page.
27. J. -H. Evertse and N. Hirata-Kohno, Wirsing systems and resultant inequalities,
    In: The Proceedings Number Theory of the New Millennium (ed. M. A. Bennett et al.), vol. 1 (2002), 449--461, book page.
28. N. Hirata-Kohno, Approximations simultanees sur les groupes algebriques commutatifs, Compositio Math., vol. 86, (1993), 69--96, , journal page.
29. N. Hirata-Kohno, Formes lineaires de points algebriques sur les groupes algebriques,
    Invent. Math., vol. 104, (1991), 401--433, journal page.
30. N. Hirata-Kohno, Formes lineaires d'integrales elliptiques, Progress in Math., vol. 91, (1990), 117--140.
31. N. Hirata-Kohno, Mesures de transcendance pour les quotients de periodes d'integrales elliptiques,
    Acta Arithmetica, vol. 56, No. 2 (1990), 111--133, journal page.
    
    

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32. Y. Bugeaud and N. Hirata-Kohno, Effective measures of linear independence for logarithms and elliptic logarithms of rational numbers, in preparation.
33. N. Hirata-Kohno, Linear forms in p-adic elliptic logarithms, in preparation.
34. N. Hirata-Kohno, S-integer points on elliptic curves via p-adic elliptic logarithms, in preparation.
35. N. Hirata-Kohno and M. Kawashima, Diophantine approximations, Book, in preparation.
36. N. Hirata-Kohno and M. Kawashima, 無理数の不思議, Book, in preparation.

List of awards

1. Next Green Inovation Conference, Poster award, 2014
2. Nistep award, 2008, National Institute of Science and Technology Policy, Ministry of Education, Culture, Sports, Science and Technology (MEXT), 2008
3. Research Prize, Science and Technology, Nihon University, 1995

Approximation diophantienne et transcendance 2018

Diophantine Analysis and Related Fields 2017

January 7, 2017(Saturday) -- January 9, 2017(Monday)
held at College of Science and Technology, Nihon University,

Supported by Research Grant 2016 for Symposia by College of Science and Technology of Nihon University,
JSPS Grants-in-aid for Scientific Research (C) 26520208 & 15K04799 and
JSPS Grant-in-aid for Young Scientists (B) 15K17522
Program: DARF 2017
Abstract of Talks: DARF 2017
Photo 1: DARF 2017 (2017-01-08)
Photo 2: DARF 2017 (2017-01-08)

数学者になった学生・院生・ポスドク

金子 元（現 筑波大学准教授），川島 誠（現 明治学院大学専任講師），宮崎 隆史（現 群馬大学准教授）
Tunde Kovacs（現 ハンガリーブダペスト工科大学准教授），David Adam（現 フランスアミアン大学），
Anthony Poels（現 フランスリヨン大学准教授），伊藤 勝（現 日本大学助教），野田 工（現 日本大学教授）

修士課程の院生

Abstract of Works

Let us consider an elliptic curve defined over a number field. Let v be a non-zero complex number whose image
by the normalized exponential map of the elliptic curve is rational. We call such v an elliptic logarithm.
As joint works of Sinnou David, we obtained the best possible lower bound of the absolute value of linear forms in
such elliptic logarithms with algebraic coefficients.
Our lower bound gives an approximation that was conjectured by S. Lang dating back to 1964. It is known that
such a lower bound is available to determine the integer points on elliptic curves.
With Sinnou David and Makoto Kawashima, we have also recently proven the irrationality
and the linear independence of polylogarithms of algebraic numbers as well as those for values
at rational points of hypergeometric functions by means of Pade approximation.
We have applied these Pade approximations to improve Evertse' bound of the number of the solutions to
the S-unit equation in 2 variables (joint work with Makoto Kawashima, Anthony Poels, and Y. Washio).

Grant-in-Aid for Scientific Research

No. of Researcher=90215195

1. Grant-in-Aid for Scientific Research (C)
   for 2021-2025 (No.of Subject=21K03171)
2. Grant-in-Aid for JSPS Fellows
   for 2021-2022 (No.of fellow=PE20746)
3. Grant-in-Aid for Scientific Research (C)
   for 2018-2021 (No.of Subject=18K03225)
4. Grant-in-Aid for Scientific Research (C)
   for 2015-2018 (No.of Subject=15K04799)
5. Grant-in-Aid for Scientific Research (C)[Generative Research Fields]
   for 2014-2017 (No.of Subject=26520208)
6. Grant-in-Aid for JSPS Fellows
   for 2013-2015 (No.of fellow=P12806)
7. NEXT Program of the JSPS for 2010-2013 (No.of Subject=GR 087) NEXT Program page.
8. Grant-in-Aid for Scientific Research (C)
   for 2010-2010 (No.of Subject=22540034)
9. Grant-in-Aid for Scientific Research (C)
   for 2007-2009 (No.of Subject=19540053)
10. Grant-in-Aid for JSPS Fellows
    for 2005-2006 (No.of Subject=17005293)
11. Grant-in-Aid for Scientific Research (C)
    for 2004-2007 (No.of Subject=16540044)
12. Grant-in-Aid for Scientific Research (C)(2)
    for 2000-2003 (No. of Subject=12640042)
13. Grant-in-Aid for Scientific Research (C)(2)
    for 1997-1998 (No.of Subject=09640069)
14. Grant-in-Aid for Scientific Research on Priority Areas
    for 1996 (No.of Subject=08211259)
15. Grant-in-Aid for Scientific Research (C)(2)
    for 1994-1996 (No.of Subject=06640082)