扈培础

扈培础的个人简介

扈培础，生于1961年8月，山东青州人。1978年至1985年在山东大学数学系计算数学专业和基础数学专业分别读本科生和研究生，获学士学位（1982）和硕士学位（1985）。1998年任山东大学数学学院教授，2003年开始任山东大学数学学院基础数学研究所所长。

简介

生于1961年8月，山东青州人。1978年至1985年在山东大学数学系计算数学专业和基础数学专业分别读本科生和研究生，获学士学位（1982）和硕士学位（1985）。1996年获香港科技大学博士学位，1998年博士后出站时破格聘为山东大学教授，1999年被聘为博士生导师。山东省、中国、美国等数学会会员。分析应用和计算国际学会（ISAAC）终身会员。印度数学杂志JAA编委。美国数学会《Math. Reviews》评论员。欧洲数学会《Zbl. Math.》评论员。

科研成就

在复分析、动力系统、数论等若干基础数学领域发表了70余篇的学术论文, 其中SCI论文10余篇。出版英文专著4部。1999年, 荣获山东省科技进步奖、二等奖和分析应用和计算国际学会(简称ISAAC)数学研究杰出成就奖。扈培础及其合作者在Kluwer学术出版社出版的两部专著中系统的总结了复域和非阿基米德域上的全纯映射值分布理论 ，其中包括许多他们的最新研究成果，例如建立了多复变亚纯函数唯一性象集理论并提出了几个引起W. Cherry、C. C. Yang等人关注的猜想；证明了ABC猜想在值分布论中对应物；提出了值分布论中Griffiths和Lang的猜想在非阿基米德全纯曲线的对应物；证明了映入一般型（或拟典则）投影簇全纯曲线退化的Green-Griffiths猜想。扈培础和杨重骏提出了广义ABC猜想、广义Hall猜想和一般的Fermat猜想并证明了在函数论中对应物；提出了Schmidt子空间定理在齐次多项式形式的猜想并在近期用P. Corvaja和U. Zannier的方法给出一个证明。扈培础和杨重骏研究了非阿基米德域和高维空间上的动力系统并提出若干问题。例如证明了射影空间上可交换的全纯映射有相同的Julia集；给出并建议了高维空间上Julia集非空的若干条件；提出了Fatou分支具有Kobayashi双曲性的猜想等。

项目

2010―2013，关于全纯映射的几个问题及相关应用，山东省自然科学基金面上项目，负责人2004―2006，ABC猜想及相关问题，国家自然科学基金面上项目，负责人2000―2002，多变量复分析和非阿基米德分析中的问题，国家自然科学基金面上项目，负责人

论著

(with C. C. Yang) The second main theorem of holomorphic curves into projective spaces, Trans. AMS. S 0002-9947(2011)05394-8.(with Z. Ye) A bound for the discriminant of number fields, Proc. Amer. Math. Soc. 139 (2011), 2007-2008.(with B. Q. Li) On meromorphic solutions of nonlinear partial differential equations of first order, Journal of Mathematical Analysis and Applications Volume 377, Issue 2, 15 May 2011, Pages 881-888.(with D. W. Meng) Normality criteria of meromorphic functions sharing one value, Journal of Mathematical Analysis and Applications Volume 377, Issue 2, 15 May 2011, Pages 881-888.On Griffiths-Langu2019 conjecture and related topics, Complex Variables and Elliptic Equations 56 (2011), 345-361.(with C. C. Yang) A linear homogeneous partial differential equation with entire solutions represented by Bessel polynomials, Journal of Mathematical Analysis and Applications 368(2010), 263-280.(with B. Q. Li) Unicity of meromorphic solutions of partial differential equations, Journal of Mathematical Sciences 173 (2011), 201-206; Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 67, Partial Differential Equations, 2010.(with C. C. Yang) Global solutions of homogeneous linear partial differential equations of the second order, Michigan Math. J. 58(2009), 807-831.(with D. W. Meng) Normality criteria of meromorphic functions with multiple zeros, Journal of Mathematical Analysis and Applications 357(2009), 323-329.(with C. Meng) Entire functions and their derivatives share two finite sets, Kyungpook Math. J. 49(2009), 473-481.(with C. C. Yang) Uniqueness theorems of meromorphic functions in several complex variables, Scientific Bulletin of Belgorod State University No.13 (68). Issue 17/1 (2009), 45-52.(with C. C. Yang) Rothu2019s theorem and $abc$-conjecture, Journal of Shandong University (Natural Science) 44 (8)(2009), 1-12.(with C. C. Yang) Distribution theory of algebraic numbers, de Gruyter Expositions in Mathematics 45, Walter de Gruyter, 2008.Introduction of functions of one complex variable (Chinese), Science Press, Bejing, 2008.(with C. C. Yang) Hyperbolic hypersurfaces of lower degrees, Some Topics on Value Distribution and Differentiability in Complex and p-adic Analysis, edited by A. Escassut, W. Tutschke and C. C. Yang, Mathematics Monograph Series 11, Science Press, Beijing, 2008, 219-234.(with C. C. Yang) Subspace theorems for homogeneous polynomial forms, Israel Journal of Mathematics 157 (2007), 47-61.(with Q. Han) Unicity of meromorphic functions related to their derivatives, Bull. Berg. Math. Soc. Simon Stevin 14 no. 5(2007), 905-918.(with C. C. Yang) Value distribution theory related to number theory, Birkh”auser, 2006.(with C. C. Yang) Unique range sets of meromorphic functions on $mathbb{C}^m$, Complex Variables and Elliptic Equations, 51(2006), 871-911.(with C. C. Yang) A note on Browkin-Brzeziu2019nski conjecture, Contemporary Mathematics 384 (2005), 101-109.(with C. C. Yang) Value distribution theory and Diophantine approximation, Analysis in Theory and Applications 21 (2) (2005), 101-117.(with C. C. Yang) Generalized Fermat and Hallu2019s conjectures, Methods of Complex and Clifford Analysis (Proceedings of ICAM, Hanoi, 2004).(with C. C. Yang) Jet bundles and its applications in value distribution of holomorphic mappings, Value Distribution Theory and Related Topics (Edited by G. Barsegian, I. Laine, C. C. Yang), Advances in Complex Analysis and Its Applications Vol. 3, pp. 281-319, Kluwer Academic Publishers, 2004.(with C. C. Yang) Nevanlinna theory and Diophantine approximations, Finite and Infinite Dimensional Complex Analysis and Applications (edited by Le Hung Son, W. Tutschke, C. C. Yang), Advances in Complex Analysis and Its Applications Vol. 2, pp. 1-19, Kluwer Academic Publishers, 2004.(with P. Li and C. C. Yang) Unicity of meromorphic mappings, Kluwer Academic Publishers, 2003.(with C. C. Yang) Unique range sets of non-Archimedean meromorphic functions, Southeast Asian Bulletin of Mathematics 27(2003), 1-18.(with X. L. Wang) Waringu2019s problem over non-Archimedean meromorphic function fields, Mathematica Applicata (Special Issue, Chinese) 16(2003), 18-21.(with C. C. Yang) A note on the $abc$-conjecture, Communications on Pure and Applied Mathematics, Vol. LV (2002), 1089-1103.(with C. C. Yang) A generalized $abc$-conjecture over function fields, J. Number Theory 94 (2002), 286-298.(with C. C. Yang) Some progress in non-Archimedean analysis, Contemporary Mathematics Vol. 303 (2002), 37-50.(with C. C. Yang) Recent topics of dynamics in high Dimensional spaces, Complex Variables 43 (2001), 325-339.(with C. C. Yang) Notes on a generalized $abc$-conjecture over function fields, Annales Mathematiques Blaise Pascal 8 (1) (2001), 61-71.(with C. C. Yang) Meromorphic Functions over non-Archimedean Fields, Kluwer Academic Publishers, 2000.(with C. C. Yang) The “abc” conjecture over function fields, Proc. Japan Acad. 76, Ser. A(2000), 118-120.(with C. C. Yang) Defect relations for moving targets, Proceedings of the Second ISAAC Congress (edited by H. G. W. Begehr, R. P. Gilbert and J. Kajiwara), Vol. 1, 271-297, Kluwer Academic Publishers, 2000.(with S. Mori) Elimination of defects of non-Archimedean holomorphic curves, Proceedings of the Second ISAAC Congress (edited by H. G. W. Begehr, R. P. Gilbert and J. Kajiwara), Vol. 1, 433-449, Kluwer Academic Publishers, 2000.(with C. C. Yang) Differentiable and complex dynamics of several variables (book), Kluwer Academic Publishers, 1999.(with C. C. Yang) A survey on $p$-adic Nevanlinna theory and its applications to differential equations, Taiwanese J. of Math. 3 (1) (1999), 1-34.(with C. C. Yang) On fixed points and factorization of meromorphic mappings, Complex Variables 38 (1999), 155-173.Non-Archimedean dynamics, Research Reports of the Nevanlinna Theory and its Applications II, Nippon Institute of Technology, 1999, 36-41.Value sharing problems in value distribution theory, Research Reports of the Nevanlinna Theory and its Applications II, Nippon Institute of Technology, 1999, 31-36.(with C. C. Yang) A unique range set of $p$-adic meromorphic functions with $10$ elements, Acta Mathematica Vietnamica 24 (1) (1999), 95-108.(with C. C. Yang) Fatou-Julia theory in differentiable dynamics, Recent Developments in Complex Analysis and Computer Algebra (R. P. Gilbert et al. (eds.)), Kluwer Academic Publishers, 1999, 113-132.(with C. C. Yang) Dynamics of composite mappings, Proc. Japan Acad. 74(1998), 146-148.(with C. C. Yang) Notes on second main theorems, Complex Variables 37 (1-4) (1998), 251-277.(with C. C. Yang) Invariant sets in dynamics, Bulletin of the Hong Kong Math. Soc. 2(1998), 75-88.Value distribution theory of non-Archimedean meromorphic functions, Post-doctoral Research Reports of Shandong University, 1998.(with C. C. Yang) Open problems of dynamics in higher dimensional spaces, In “Open problems for the Workshop on Value Distribution Theoery and its Applications” edited by A. F. Beardon and C. C. Yang, Hong Kong, July 1996, Izvestiya Natsionalnoi Akademii Nauk Armenii. Matematika 32(4) (1997), 9-36.(with C. C. Yang) The Cartan conjecture for $p$-adic holomorphic curves, Technical Report, The Hong Kong Univ. of Sci. & Tech., 1997; Izvestiya Natsionalnoi Akademii Nauk Armenii. Matematika 32 (4) (1997), 45-80.(with C. C. Yang) Value distribution theory of $p$-adic meromorphic functions, Technical Report, The Hong Kong Univ. of Sci. & Tech., 1997; Izvestiya Natsionalnoi Akademii Nauk Armenii (National Academy of Sciences of Armenia) 32 (3)(1997), 46-67.Value distribution theory and complex dynamics, Bulletin of the Hong Kong Math. Soc. Vol.1 No.1(1997), 169-172.(with C. C. Yang) Value distribution theory and its applications to meromorphic mappings (Part 2), Journal of the National Institute for Compilation and Translation (Taiwan) 26 (1) (1997), 355-427.(with C. C. Yang) Value distribution theory and its applications to meromorphic mappings (Part 1), Journal of the National Institute for Compilation and Translation (Taiwan) 25 (2) (1996), 321-388.(with C. C. Yang) Fatou-Julia theory in high dimensional spaces, International Workshop on The Value Distribution Theory and Its Applications, Hong Kong, 1996; Bull. of Hong Kong Math. Soc. 1 (2) (1997), 273-287.(with C. C. Yang) On the value distribution of $ff^{(k)}$, Kodai Math. J. 19(1996), 157-167; MR 97d:30042; Zbl. Math. 867(1997), 30023, p. 149.(with C. C. Yang) Further results on factorization of meromorphic solutions of partial differential equations, Results in Mathematics 30(1996), 310-320; MR 98f:32003; Zbl. Math. 866(1997), 32006, p. 153.(with C. C. Yang) Uniqueness of meromorphic functions on $mathbb{C}^m$, Complex Variables 30(1996), 235-270; MR 97g:32004; Zbl. Math. 859(1997), 32002, p. 163.(with C. C. Yang) Applications of pseudo volume forms to holomorphic mappings, Complex Variables 30(1996), 153-168; MR 98b:32022; Zbl. Math. 856(1997), 32001, p. 189.Value distribution theory and complex dynamics, PhD thesis, The Hong Kong University of Science and Technology, 1996.(with C. C. Yang) The second main theorem for algebroid functions of several complex variables, Math. Z. 220(1995), 99-126; MR 96j:32001; Zbl. Math. 826(1996), 32001, p. 162.(with C. C. Yang) Malmquist type theorem and factorization of meromorphic solutions of partial differential equations, Complex Variables 27(1995), 269-285; MR 96g:32006; Zbl. Math. 841(1996), 32002, p. 170.(with C. C. Yang) Factorization of holomorphic mappings, Complex Variables 27(1995), 235-244; MR 96f:32004; Zbl. Math. 841(1996), 32001, p. 170.Holomorphic mappings between spaces of different dimensions II, Math. Z. 215(1994), 187-193; MR 95a:32046; Zbl. Math. 791(1994), 58015, p. 356.Holomorphic mappings between spaces of different dimensions I, Math. Z. 214(1993), 567-577; MR 94k:32043; Zbl. Math. 791(1994), 58014, p. 356.(with M. Z. Yang) A theorem of differential mappings of Riemann surfaces, Internat. J. Math. & Math. Sci. (1)17(1994), 189-192; MR 94k:30103; Zbl. Math. 801(1995), 30037, p. 149.An extension of Haymanu2019s inequality II, J. of Shandong University (2)29(1994), 121-126; MR 96a:30037; Zbl. Math. 813(1995), 30025, p. 154.(with C. C. Yang) Pseudo volume forms and their applications to holomorphic mappings, Proc. Japan Acad. (A-5)69(1993), 149-153; MR 94h:32043; Zbl. Math. 811(1995), 32017, p. 164.Value distribution and admissible solutions of algebraic differential equations, J. of Shandong University (2)28(1993), 127-133; MR 94h:30040; Zbl. Math. 784(1994), 30026, p. 129.Haymanu2019s points of holomorphic functions, J. of Shandong University (4)27(1992), 419-424; MR 94b:30037.(with L. Z. Yang) Admissible solutions of algebraic differential equations, J. of Shandong University (1)26(1991), 19-25; MR 93g:34009; Zbl. Math. 744(1992), 34006, p. 194.(with T. Wen) On some problems of value distribution for several variables, J. of Binzhou Teachers College (4)7(1991), 1-5.Holomorphic mappings into algebraic varieties of general type II, Nagoya Math. J. 120(1990), 171-180; MR 92b:32033; Zbl. Math. 702(1991), 32027, p. 154.Holomorphic mappings into algebraic varieties of general type, Nagoya Math. J. 120(1990), 155-170; MR 92b:32033; Zbl. Math. 702(1991), 32026, p. 154.(with T. Wen) Aspects of value distribution theory for holomorphic mappings on complex manifolds, Advances in Math. (PRC) (4)19(1990), 385-395; MR 91h:32022; Zbl. Math. 724(1992), 32011, p. 145.A modified defect relation for holomorphic curves, Kodai Math. J. (3)13(1990), 349-362; MR 91m:32026; Zbl. Math. 736(1992), 32019, p. 147.The properties of the zero points distribution for the Riemannu2019s Zeta function, Pure & Applied Math.(PRC) (2)6(1990), 6-12; MR 96b:11121; Zbl. Math. 862(1997), 11049, p. 71.An extension of Haymanu2019s inequality, J. of Math.(PRC) (4)10(1990), 405-412; MR 92c:30033; Zbl. Math. 734(1992), 30031, p. 120-121.A generalization of Chang-Yang Theorem, J. of Shandong University (2)25(1990), 137-147; Zbl. Math. 707(1991), 30027, p. 111.An application of the Carleman formula, Hunan Annals of Math.(PRC) (1-2)10(1990), 152-156; MR 92j:11089; Zbl. Math. 776(1994), 11049, p. 59.(with T. Wen) On Chernu2019s First Main Theorem of holomorphic maps, The Symposium to Min Sihe, Shandong Univ. Press, 1990, 16-23.One characteristic function of meromorphic functions, J. of Yunmeng (Natural Science) (3)43(1990), 1-10.Order and Borel directions of an essential sigularity, J. of Shandong University 23 (1988), 9-14; Zbl. Math. 681(1990), 30018, p. 110.Meromorphic functions in angular domains, J. of Shandong University (3)23(1988), 1-8; Zbl. Math. 679(1990), 30025, p. 118.Meromorphic functions in angular domains, the Postgraduate Office of Shandong University, 1985.A sufficient and necessary condition on Riemann Conjecture, the Postgraduate Office of Shandong University, 1985.Some applications of Carleman Formula, the Postgraduate Union of Shandong University, 1984.