摘要
1920年,印度天才数学家斯里尼瓦瑟·拉马努金(Srinivasa Ramanujan)在给英国数学家G.H.Hardy的最后一封信中提到了被他命名的17个"mock theta函数",在其之后的近80余年中,关于这些神秘函数的本质属性没有实质性突破。直到2002年,S.P.Zwegers在导师D.Zagier指导下完成的博士论文中,首次揭开了mock theta函数具有的模形式本质属性。这使其成为近10年来国际数学领域研究的热点问题。文章基于这一领域的文献研究和成果,对mock theta函数的研究背景、研究进展、最新研究成果等理论和方法做一综述。
In 1920,the India genius mathematician SrinivasaRamanujangave hislast letter to the British mathematician G. H.Hardy while 17 functions were mentioned by himwhich were named"mock theta functions".After nearly more than eighty years,the nature property of these mysterious functions had no substantive breakthrough. Until 2002,S.P. Zwegerscompleted his doctoral thesis under the guidance of his tutor D. Zagierand he first revealed the natural modular form property for the mock theta functions. This result has made it to be the hot problems in the international mathematics research field nearly the recent 10 years. This paper is based on the studying of the literature and the research results of this field in recent years,to give some reviews on the background,progress,and the latest research theory and methods of the mock theta functions.
出处
《渭南师范学院学报》
2018年第4期23-29,共7页
Journal of Weinan Normal University
基金
国家自然科学基金项目:Mock模形式的构造研究及其在密码学中的应用(61402335)
陕西省科技厅自然科学基金项目:Mock theta函数理论及其交叉应用研究(2016JM1004)
陕西省教育厅专项科研计划项目:Ramanujan mock theta函数的算数性质及其应用研究(17JK0860)
渭南师范学院人才项目:Mock theta函数理论及其进展研究(17ZRRC01)
渭南师范学院教育教学改革研究项目:中俄数学文化中的国际化人才培养模式研究(JG201622)
