My Research (Including Publication List)

[ English | Japanese ]

Research Interest

My research interests are Modular forms, Automorphic forms, Jacobi forms, and their ring structure.

Papers in MathSciNet

Refereed Papers

  1. Aoki, H. and Saito, K., Modular forms from the Weierstrass functions, Pure and Applied Mathematics Quarterly 16-4(2020) 967-980.
  2. Aoki, H., Generalization of the Weierstrass p function and Maass lifts of weak Jacobi forms, Pure and Applied Mathematics Quarterly 16-3(2020) 371-420.
  3. Aoki, H. and Takemori, S., The structure of mixed weight Hilbert modular forms, Int. J. Math. 30-2(2019).
  4. Aoki, H., On Jacobi forms of real weights and indices, Osaka J. Math. 54-3(2017), 569-585.
  5. Aoki, H., On Siegel paramodular forms of degree 2 with small levels, Int. J. Math. 27-2(2016).
  6. Aoki, H., On vector valued Siegel modular forms of degree 2 with small levels, Osaka J. Math. 49-3(2012), 625-651.
  7. Aoki, H., Estimate of the dimensions of mixed weight Hilbert modular forms, Commun. Math. Univ. St. Pauli. 57-1(2008), 1-11.
  8. Akahori, J., Aoki, H. and Nagata, Y., Generalizations of Ho-Lee's binomial interest rate model I: from one- to multi-factor, Asia Pacific Financial Markets 13-2(2006), 151-179.
  9. Aoki, H. and Ibukiyama, T., Simple Graded Rings of Siegel Modular Forms, Differential Operators and Borcherds Products, Int. J. Math. 16-3(2005), 249-279.
  10. Aoki, H., The graded ring of Hermitian modular forms of degree 2, Abh. Math. Sem. Univ. Hamburg. 72(2002), 21-34.
  11. Aoki, H., Estimating Siegel modular forms of genus 2 using Jacobi forms, J. Math, Kyoto Univ. 40-3(2000), 581-588.
  12. Aoki, H., Automorphic forms on the expanded symmetric domain of type four, Publ. RIMS, Kyoto Univ. 35(1999), 263-283. (pubrims1.dvi)

Talks at International Conference

  1. Aoki, H., On the structure theorem for modular forms ... Igusa’s result and beyond, Local zeta functions and the arithmetic of moduli spaces: A conference in memory of Jun-Ichi Igusa, Johns Hopkins University, Baltimore, USA, 2017. (slides...jamiaoki.pdf)
  2. Aoki, H., On formal series of Jacobi forms and Borcherds products, International Workshop on Mathematics in Oman 2012, Sultan Qaboos University, Muscat, Oman, 2012.
  3. Aoki, H., On mixed weight Hilbert modular forms, Jacobi forms and applications, CIRM, Luminy, Marseille, France, 2007. (resume...luminy2.dvi)
  4. Aoki, H., Jacobi forms, Fourier-Jacobi development, and the ring structure of automorphic forms, Jacobi forms and applications, CIRM, Luminy, Marseille, France, 2001. (resume...luminy1.dvi)

Proceedings

  1. Aoki, H., On mixed weight Hilbert modular forms and their structure theorem, Analytic and Arithmetic Theory of Automorphic Forms (Kyoto, 2018), S\=urikaisekikenky\=usho K\=oky\=uroku 2100, 65-79.
  2. Aoki, H., On formal Series of Jacobi Forms and Borcherds Products, Automorphic Forms, Springer Proceedings in Mathematics and Statistics (PROMS) 115 (2015), 1-10.
  3. Aoki, H., On Jacobi forms which connect infinite products and infinite sums, Research on Finite Groups and Their Representations, Vertex Operator Algebras, and Algebraic Combinatorics (Kyoto, 2014), S\=urikaisekikenky\=usho K\=oky\=uroku 1965, 30-44.
  4. Aoki, H., Determination of the structure of vector valued Siegel modular forms by using Jacobi forms, 2014 Number Theory Workshop at Waseda University (Waseda, 2014), 88-97. (waseda14.pdf)
  5. Aoki, H., On Jacobi Forms with Levels, Number Theory - Arithmetic in Shangri-la, Proceedings of the 6th China-japan Seminar, Series on Number Theory and Its Applications vol.8 (2013), 1-16.
  6. Aoki, H., On Index-Level change of Jacobi forms (joint work with N.-P. Skoruppa and H. Sakata), 2012 Number Theory Workshop at Waseda University (Waseda, 2012), 66-77. (waseda12.pdf)
  7. Aoki, H., Borcherds lift, 19th Summer School on Number theory (Hakone, 2011), 212-241. (ss11aoki.pdf)
  8. Aoki, H., A remark on Borcherds construction of Jacobi forms, 5th Fukuoka Symposium on Number Theory (Kyushu, 2010), 11-22. (kyushu.pdf)
  9. Aoki, H., Vector valued Siegel modular forms with small levels, Automorphic Representations, Automorphic Forms, L-functions, and Related Topics (Kyoto, 2008), S\=urikaisekikenky\=usho K\=oky\=uroku 1617, 167-177.
  10. Aoki, H., On the ring structure of modular forms, Seminar at Josai Univ., Josai Univ., 2007. Mathematical Bullet of the Graduate School of Science, Josai University 10(2007), 70-82. (josai.dvi)
  11. Aoki, H., On the ring structure of Siegel modular forms, NPU-TUS Bilateral Seminar, Northwestern Polytechnical Univ. (Xi'an, China), 2006. (xian.dvi)
  12. Aoki, H., Estimate of the dimension of Hilbert modular forms by means of differential operator, Automorphic forms and Zeta functions (Rikkyo, 2004), Proceedings of the Conference in Memory of Tsuneo Arakawa, World Scientific, 20-28.
  13. Aoki, H., Practical Construction of Borcherds Product, The first spring conference on automorphic forms (Hamanako, 2002), 97-112. (hamana1.dvi)
  14. Aoki, H., Estimating the dimension of the space of Siegel modular forms of genus 2 withe level 2 and 3, Proceedings of Japan-German seminar, Explicit Structure of Modular Forms and Zeta Functions (Hakuba, 2001), 101-106. (hakuba2.dvi)
  15. Aoki, H., Estimation of the dimension of modular forms by using Jacobi forms, Codes, Lattices, Modular forms and Vertex operator algebras (Yamagata, 2000), 48-52. (yamagata1.dvi)
  16. Aoki, H., New approach to dimension formula using Jacobi forms, The third autumn workshop on number theory (Hakuba, 2000), 93-108. (hakuba1.dvi)
  17. Aoki, H., Automorphic forms on the expanded symmetric domain of type IV, Automorphic forms and L-functions (Kyoto, 1999), S\=urikaisekikenky\=usho K\=oky\=uroku 1103, 8-14.
  18. Aoki, H., An automorphic forms on the expanded symmetric domain of type IV (introductory talk), Singularities and complex analytic geometry (Kyoto, 1997), S\=urikaisekikenky\=usho K\=oky\=uroku 1033, 148-153.

Talks

  1. Aoki, H., Automorphic forms from the Weierstrass p function (joint work with Kyoji Saito), 2020 Seminar on Number Theory at Oita, Zoom meeting, 2020.
  2. Aoki, H., Formal series of Jacobi forms, Oberseminar Institut fuer Algebraische Geometrie, Leibniz Universitaet Hannover, 2020.
  3. Aoki, H., The theory and application of Jacobi forms Joint meeting of Tohoku University and Tokyo University of Science, Tokyo University of Science, 2020.
  4. Aoki, H., Equations between infinite products and infinite sums and automorphic forms, 1st Seminar on Number Theory at Oita, Oita University, 2019.
  5. Aoki, H., A short survey on elliptic modular forms, IPMU Special Seminar `Elliptic Artin groups I, II', IPMU, 2019.
  6. Aoki, H., On Maass lifts of weak Jacobi forms, Seminar on automorphic forms in Mannheim University, Mannheim University (Mannheim, Germany), 2019.
  7. Aoki, H., A generalization of the Weierstrass p function and Maass lift of weak Jacobi forms, 2018 Seminar on Number Theory at Oita and Kagoshima, Kagoshima University, 2018.
  8. Aoki, H., On Maass lift of weak Jacobi forms, Number theory seminar, Kyoto University, 2018.
  9. Aoki, H., On the construction and the determination of the total space of mixed weight Hilbert modular forms, Automorphic forms/representaions on covering groups, Okayama University, 2018.
  10. Aoki, H., On the structures of mixed weight Hilbert modular forms on real quadratic fields, Workshop On Jacobi Forms and Applications, University of Nottingham (UK), 2018.
  11. Aoki, H., On the structure of mixed weight Hilbert modular forms, Seminar Aachen-Bonn-Koeln-Lille-Siegen on Automorphic Forms, Max-Planck-Institut fuer Mathematik (Germany), 2017.
  12. Aoki, H., Introduction to Jacobi forms, Kagurazaka algebra seminar, Tokyo University of Science (Tokyo), 2017.
  13. Aoki, H., Easy application of elementary algebra to Hilbert modular forms, Kyushu University algebra seminar, Kyushu University (Fukuoka), 2017.
  14. Aoki, H., On the structure of Hilbert modular forms with discriminant 5, Oberseminar Modulfunktionen, Heidelberg University (Heidelberg, Germany), 2016.
  15. Aoki, H., A remark on the structure of mixed weight Hilbert modular forms, Seminar on automorphic forms in Mannheim University, Mannheim University (Mannheim, Germany), 2016.
  16. Aoki, H., Jacobi forms as infinite products, Niigata algebra seminar, Niigata University (Niigata), 2016.
  17. Aoki, H., Jacobi forms as infinite products, Aichi seminar on number theory, Nagoya Institute of Technology (Nagoya), 2016.
  18. Aoki, H., On Jacobi forms of real weights and indices, Seminar on number theory and automorphic forms in Osaka University, Osaka University (Toyonaka), 2016.
  19. Aoki, H., A remark on the weights of Siegel modular forms, 30th Automorphic Forms Workshop, Wake Forest University, Winston-Salem, NC, USA., 2016.
  20. Aoki, H., A remark on the weights of modular forms, Seminar on automorphic forms in Mannheim University, Mannheim University (Mannheim, Germany), 2015.
  21. Aoki, H., Jacobi forms of fractional weights and indices, Kagawa Seminar, Kagawa University (Takamatsu), 2015.
  22. Aoki, H., Jacobi forms which associate equations between infinite products and infinite sums, Combinatorics Seminar, Tohoku University (Sendai), 2015.
  23. Aoki, H., Structure theorem of the space of automorphic forms of several variables, The 17th autumn workshop on number theory, Hakuba, 2014.
  24. Aoki, H., Estimation of the dimension of modular forms of several variables, Oberseminar Modulfunktionen, Heidelberg University (Heidelberg, Germany), 2014.
  25. Aoki, H., On the structure of mixed weight Hilbert modular forms, Seminar on automorphic forms in Mannheim University, Mannheim University (Mannheim, Germany), 2014.
  26. Aoki, H., On Jacobi forms of rational weight and rational index, 28th Automorphic Forms Workshop, Moab Arts and Recreation Center, Moab, UT, USA., 2014.
  27. Aoki, H., Some Problems on Jacobi Forms, Seminar on automorphic forms in Tongji University, Tong Ji University (Shanghai, China), 2014.
  28. Aoki, H., Jacobi forms of rational weight and rational index, Explicit Theory of Automorphic Forms, Tong Ji University (Shanghai, China), 2014.
  29. Aoki, H., On Jacobi forms of fractional weight, The 7th China-Japan Conference on number theory, Kyushu Univ., 2013.
  30. Aoki, H., On Maass lift to Siegel paramodular forms, Workshop on Modular Forms and Jacobi Forms, Joetsu University of Education, 2013.
  31. Aoki, H., On Siegel paramodular forms of degree 2 with small levels, 27th Automorphic Forms Workshop, University College Dublin, Dublin, Ireland, 2013.
  32. Aoki, H., On modular forms of the Siegel paramodular group, Workshop on Modular Forms, Kyushu Univ., 2012.
  33. Aoki, H., On Siegel paramodular forms, Saturday Seminar at Gakushuin Univ., Gakushuin Univ., 2012.
  34. Aoki, H., On the construction of Jacobi forms by using infinite products by Borcherds, KSU seminar on Number Theory, Kyoto Sangyo Univ., 2012.
  35. Aoki, H., On Index-Level change of Jacobi forms (Part 2)(joint work with H. Sakata), Number Theory Seminar at Waseda Univ., Waseda Univ., 2012.
  36. Aoki, H., On index-level change of Jacobi forms, 26th Automorphic Forms Workshop, University of British Columbia, Vancouver, BC, Canada, 2012.
  37. Aoki, H., Level Index change of Jacobi forms, Saturday Seminar at Gakushuin Univ., Gakushuin Univ., 2011.
  38. Aoki, H., Some results on Jacobi forms, Seminar on number theory at Muroran Institute of Technology, Muroran Institute of Technology, 2011.
  39. Aoki, H., On Jacobi Triple Product Identity and Borcherds Products, Seminar on automorphic forms in Tongji University, Tong Ji University (Shanghai, China), 2011.
  40. Aoki, H., On the convergence of formal Fourier-Jacobi expansion, The 6th China-Japan Conference on number theory, Shanghai Jiao Tong University (Shanghai, China), 2011.
  41. Aoki, H., On Duursma zeta functions and the Riemann hypothesis, Saturday Seminar at Gakushuin Univ., Gakushuin Univ., 2011.
  42. Aoki, H., On the Jacobi Triple Product Identity and Borcherds Products, Seminar Aachen-Koeln-Lille-Siegen on Automorphic Forms, Uni. Siegen (Germany), 2010.
  43. Aoki, H., A remark on Borcherds construction of Jacobi forms, Saturday Seminar at Gakushuin Univ., Gakushuin Univ., 2010.
  44. Aoki, H., On Borcherds infinite products, Seminar at Nara Women's University, Nara Women's University, 2010.
  45. Aoki, H., On the image of Fourier-Jacobi expansion, 24th Automorphic Forms Workshop, University of Hawaii at Manoa, Honolulu, HI, USA., 2010.
  46. Aoki, H., On the convergence of Fourier-Jacobi expansion, Geometry of lattices and infinite dimensional Lie algebras, IPMU, the Univ. of Tokyo, 2010.
  47. Aoki, H., On the Jacobi triple product; On Borcherds infinite products (1)(2), Project seminar at Kumamoto, Kumamoto Univ, 2010.
  48. Aoki, H., On the Jacobi triple product, Seminar at IPMU, the Univ. of Tokyo, 2010.
  49. Aoki, H., On the Jacobi triplet product identity, Saturday Seminar at Gakushuin Univ., Gakushuin Univ., 2010.
  50. Aoki, H., About the convergence of formal series of Jacobi forms, Mathematisches Kolloquim, Uni. Siegen (Germany), 2009.
  51. Aoki, H., Formal series of Jacobi forms and Maass lifts of weak Jacobi forms, Seminar at Nara Women's Univ., Nara Women's Univ., 2009.
  52. Aoki, H., Fourier-Jacobi tenkai no syuusokusei to Borcherds mugenseki (Japanese), Seminar at Tokyo Univ. of Science, Tokyo Univ. of Science, 2009.
  53. Aoki, H., Formal series of Jacobi forms, The 12th autumn workshop on number theory, Hakuba, 2009.
  54. Aoki, H., Jacobi keishiki ni kansuru syokekka no syokai - Hokeikeishiki no gutaiteki na kousei no kanten kara (Japanese), Saturday Seminar at Gakushuin Univ., Gakushuin Univ., 2009.
  55. Aoki, H., Keishiki teki na Fourier-Jacobi tenkai no syuusokusei ni tsuite (Japanese), Number Theory Seminar at Waseda Univ., Waseda Univ., 2009.
  56. Aoki, H., On Vector valued Siegel modular forms, Seminar Aachen-Koeln-Lille-Siegen on Automorphic Forms, Uni. Siegen (Germany), 2008.
  57. Aoki, H., Toward the determination of the structure of Hilbert-Siegel modular forms, Mathematisches Kolloquim, Uni. Siegen (Germany), 2008.
  58. Aoki, H., Jitsu 2 jitai jou no Hilbert hokeikeishiki no nasu kan no kouzou ni tsuite (Japanese), Seminar at Sophia Univ., Sophia Univ., 2007.
  59. Aoki, H., Vector valued Siegel modular forms with small levels, The 10th autumn workshop on number theory, Hakuba, 2007. (hakuba3.dvi)
  60. Aoki, H., Hilbert hokei keishiki no jigen no hyouka (Japanese), MSJ meetings 2005 autumn, Okayama Univ., 2005. (msj05abs.dvi), (msj05ohp.dvi)
  61. Aoki, H., Jacobi keishiki wo mochiita hokeikeishiki-kan no kouzoukettei mondai he no approach (Japanese), MSJ meetings 2004 spring, Univ. of Tsukuba, 2004. (msj04.dvi)
  62. Aoki, H., Hermitian modular forms of degree 2 with respect to the imaginary quadratic field of the discriminant -3, Seminar at Aachen Univ. (Germany), 2002.
  63. Aoki, H., Siegel modular forms of odd weights of level 3, Seminar on Number Theory and Automorphic forms, Osaka Univ., 2001.
  64. Aoki, H., Estimation of the dimension of modular forms by using Jacobi forms, Seminar on Combinatorics, Kyushu Univ., 2000.
  65. Aoki, H., Estimating Siegel modular forms of genus 2 using Jacobi forms, Mini-conference on modular forms, Osaka Univ., 2000.
  66. Aoki, H., Jacobi keishiki wo mochiita genus 2 no hokeikeishiki no seiseigen no kettei ni tsuite (Japanese), Seminar on Number Theory, Kyoto Univ., 1999.

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Last modified: Thu May 26 16:47:09 JST 2016