{"id":59,"date":"2014-12-19T01:49:18","date_gmt":"2014-12-18T16:49:18","guid":{"rendered":"http:\/\/www2.math.cst.nihon-u.ac.jp\/hirata\/?page_id=59"},"modified":"2021-05-04T09:26:18","modified_gmt":"2021-05-04T00:26:18","slug":"research","status":"publish","type":"page","link":"http:\/\/www2.math.cst.nihon-u.ac.jp\/hirata\/research","title":{"rendered":"Research"},"content":{"rendered":"

Main publications<\/h3>\n

The number of published articles: 91<\/span><\/p>\n

    \n
  1. S. David, N. Hirata-Kohno and M. Kawashima, Linear forms in polylogarithms, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, accepted for publication, (2021).<\/li>\n
  2. S. David, N. Hirata-Kohno and M. Kawashima, Can polylogarithms at algebraic points be linearly independent?, Moscow Journal of Combinatorics and Number Theory, vol. 9, no. 4, (2020), 389-406 <\/span>10.2140\/moscow.2020.9.389<\/a><\/li>\n
  3. H. Furutsu and N. Hirata-Kohno, Linear dependence criterion of almost integer valued functions: a generalization of the Polya-Pisot theorem, J. Research Institute of Science and Technology, Nihon University, (2019), 144, 12–16.<\/li>\n
  4. 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.<\/li>\n
  5. H. Furutsu and N. Hirata-Kohno, Conditions of an Analytic Function to be a Polynomial via Diophantine Approximations,\u00a0<\/span>Research Institute of Science and Technology, CST, Nihon University (2016), vol. 136, 12–16.<\/li>\n
  6. N. Hirata-Kohno and F. Luca, On the Diophantine equation $F_n^x+F_{n+1}^x=F_m^y$,\u00a0<\/span>Rocky Mountain Journal of Mathematics, Rocky Mountain Journal of Mathematics (2015), vol. 45, no. 2, 509–538 published pdf<\/span><\/a>, journal page<\/span><\/a>.<\/li>\n
  7. N. Hirata-Kohno and T. Kovacs, Computing S-integral points on elliptic curves of rank at least $3$,<\/span>RIMS Kokyuroku, Kyoto University, Vol. 1898, (2014), 92–102, published pdf<\/span><\/a>, RIMS page<\/span><\/a>.<\/li>\n
  8. N. Hirata-Kohno, Diophantine approximation related to polylogarithms,\u00a0<\/span>RIMS Kokyuroku, Kyoto University, Vol. 1898, (2014), 194–206, published pdf<\/span><\/a>, RIMS page<\/span><\/a>.<\/li>\n
  9. A. B\\’erczes, L. Hajdu, N. Hirata-Kohno, T. Kovacs and A. Peth\\H{o},<\/span>A key exchange protocol based on Diophantine equations and S-integers, JSIAM Letters, vol. 6(2014), 85–88 journal page<\/span><\/a>.<\/li>\n
  10. N. Hirata-Kohno and A. Peth\\H{o}, On a key exchange protocol based on Diophantine equations,\u00a0<\/span>Infocommunications Journal, ISSN 2061-2079, Vol. 5, (2013), No. 3, 17–21; published pdf (without photo)<\/span><\/a>, published page<\/span><\/a>.<\/li>\n
  11. M. Ito and N. Hirata-Kohno, Optimization for lattices and Diophantine approximations,\u00a0<\/span>Interdisciplonary Information Sciences, vol. 19, No. 2, (2013), 135–142.<\/li>\n
  12. N. Hirata-Kohno, Arithmetic properties of p-adic elliptic polylogarithms and irrationality,\u00a0<\/span>In: Diophantische Approximationen, Oberwolfach Report Vol. 9, Issue 2, 1347–1351, (2012), eds. Y. Bugeaud and Yu. V. Nesterenko, European Math. Society, published pdf<\/span><\/a>.<\/li>\n
  13. N. Hirata-Kohno and H. Okada, A note on linear independence of polylogarithms over the rationals,\u00a0<\/span>Proceedings of the Japan Academy, series A, 88\/9, (2012), 156–161; published pdf<\/span><\/a>.<\/li>\n
  14. N. Hirata-Kohno, Diophantus Approximations, The Mathematical Society of Japan,\u00a0<\/span>Sugaku, Iwanami, July 2012, vol. 64(3), 254–277, journal page<\/span><\/a>.<\/li>\n
  15. N. Hirata-Kohno, Arithmetic properties of p-adic elliptic logarithmic functions,\u00a0<\/span>Series on Number Theory and its Applications, vol. 7, 2011, 110–119.<\/li>\n
  16. N. Hirata-Kohno and R. Takada, Linear forms in two elliptic logarithms in the p-adic case,\u00a0<\/span>Kyushu J. of Mathematics, vol. 64, no. 2, (2010), 239–260.<\/li>\n
  17. S. David and N. Hirata-Kohno, Linear forms in elliptic logarithms,\u00a0<\/span>Journal fur die reine und angewandte Mathematik, vol. 628, (2009), 37–89.<\/li>\n
  18. N. Hirata-Kohno, S. Laishram, T. N. Shorey and R. Tijdeman, An extension of a theorem of Euler,\u00a0<\/span>Acta Arithmetica vol. 129 (1), (2007), 71–102.<\/li>\n
  19. S. David and N. Hirata-Kohno, Logarithmic Functions and Formal Groups of Elliptic Curves,\u00a0<\/span>In: Diophantine Equations (ed. N. Saradha), Tata Institute of Fundamental Research, Narosa Publishing House, India, 243–255.<\/li>\n
  20. S. David and N. Hirata-Kohno, Recent progress on linear forms in elliptic logarithms,\u00a0<\/span>A Panorama in Number Theory, (ed. G. Wuestholz), Cambridge Univ. Press (2002), 26–37.<\/li>\n
  21. J. -H. Evertse and N. Hirata-Kohno, Wirsing systems and resultant inequalities,\u00a0<\/span>In: The Proceedings Number Theory of the New Millennium (ed. M. A. Bennett et al.), vol. 1 (2002), 449–461.<\/li>\n
  22. N. Hirata-Kohno, Approximations simultanees sur les groupes algebriques commutatifs, Compositio Math., vol. 86, (1993), 69–96.<\/span><\/li>\n
  23. N. Hirata-Kohno, Formes lineaires de points algebriques sur les groupes algebriques,\u00a0<\/span>Invent. Math., vol. 104, (1991), 401–433.<\/li>\n
  24. N. Hirata-Kohno, Formes lineaires d’integrales elliptiques, Progress in Math., vol. 91, (1990), 117–140.<\/span><\/li>\n
  25. N. Hirata-Kohno, Mesures de transcendance pour les quotients de periodes d’integrales elliptiques,\u00a0<\/span>Acta Arith., vol. 56, No. 2 (1990), 111–133.<\/li>\n
  26. Y. Bugeaud and N. Hirata-Kohno, Effective measures of linear independence for logarithms and elliptic logarithms of rational numbers, Preprint.<\/span><\/li>\n
  27. N. Hirata-Kohno, Linear forms in p-adic elliptic logarithms, preprint.<\/span><\/li>\n
  28. N. Hirata-Kohno, S-integral points on elliptic curves via new approximation of p-adic elliptic logarithms, preprint.<\/span><\/li>\n
  29. N. Hirata-Kohno and M. Kawashima, Diophantine approximations, Book, in preparation.<\/span><\/li>\n<\/ol>\n

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