交错Ramanujan循环和公式的推广及其应用

删除或更新信息，请邮件至freekaoyan#163.com(#换成@)

本站小编 Free考研考试/2021-12-27

交错Ramanujan循环和公式的推广及其应用雒秋明重庆师范大学数学学院, 重庆 401331 An Extension for the Alternating Ramanujan's Circular Summation Formula and Applications LUO QiumingDepartment of Mathematics, Chongqing Normal University, Chongqing Higher Education Mega Center, Huxi Campus, Chongqing 401331

摘要
图/表
参考文献(0)
相关文章(0)
点击分布统计
下载分布统计
-->

全文: PDF(238 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要本文给出了交错Ramanujan循环和公式的一个推广并由此得到了一些新的theta函数恒等式.

服务

加入引用管理器

E-mail Alert

RSS

收稿日期: 2014-10-08

PACS:

O156

基金资助:重庆市自然科学基金(CSTC2011JJA00024),重庆市教委科技研究项目(KJ120625),重庆师范大学自然科学重点项目(10XLR017,2011XLZ07)资助.

引用本文:

雒秋明. 交错Ramanujan循环和公式的推广及其应用[J]. 应用数学学报, 2016, 39(2): 161-172. LUO Qiuming. An Extension for the Alternating Ramanujan's Circular Summation Formula and Applications. Acta Mathematicae Applicatae Sinica, 2016, 39(2): 161-172.

链接本文:

http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2016/V39/I2/161

[1]	Chandrasekharan K. Elliptic Functions. Berlin, Heidelberg: Springer-Verlag, 1985
[2]	Whittaker E T, Watson G N. A Course of Modern Analysis. ???: Cambridge University Press, 1927, 4th ed, Reprinted, 1963
[3]	Bellman R. A brief introduction to theta functions. New York: Holt, Rinehart and Winston, 1961
[4]	Ramanujan S. The Lost Notebook and Other Unpublished Papers. New Delhi: Narosa, 1988
[5]	Andrews G E, Berndt B C. Ramanujan's Lost Notebook, Part III. New York: Springer-Verlag, 2012
[6]	Chan H H, Liu Z G, Ng S T. Circular summation of theta functions in Ramanujan's Lost Notebook. J. Math. Anal. Appl., 2006, 316: 628-641
[7]	Zeng X F. A generalized circular summation of theta function and its application. J. Math. Anal. Appl., 2009, 356: 698-703
[8]	Chan S H, Liu Z G. On a new circular summation of theta functions. J. Number Theory, 2010, 130: 1190-1196
[9]	Zhu J M. An alternate circular summation formula of theta functions and its applications. Appl. Anal. Discrete Math., 2012, 6: 114-125
[10]	Zhu J. M. A note on a generalized circular summation formula of theta functions. J. Number Theory., 2012, 132: 1164-1169
[11]	Boon M, Glasser M L, Zak J., Zucker I J. Additive decompositions of υ-functions of multiple arguments. J. Phys. A: Math. Gen., 1982, 15: 3439-3440
[12]	Berndt B C. Ramanujan's Notebooks, Part V. New York: Springer-Verlag, 1998
[13]	Ahlgren S. The sixth, eighth, ninth and tenth powers of Ramanujan theta function. Proc. Amer. Math. Soc., 2000, 128: 1333-1338
[14]	Berndt B C. Ramanujan's Notebooks, Part III. New York: Springer-Verlag, 1991
[15]	Borwein J M, Borwein P B. A cubic counterpart of Jacobi's identity and the AGM. Trans. Amer. Math. Soc., 1991, 323: 691-701
[16]	Cai Y, Chen S, Luo Q M. Some circular summation formulas for the theta functions. Bound. Value Probl., 2013, 2013: 59
[17]	Chua K S. The root lattice An* and Ramanujan's circular summation of theta functions. Proc. Amer. Math. Soc., 2002, 130: 1-8
[18]	Chua K S. Circular summation of the 13th powers of Ramanujan's theta function. Ramanujan J., 2001, 5: 353-354
[19]	Gasper G, Rahma M. Basic Hypergeometric Series. Cambridge: Cambridge Unversity Press, 2004
[20]	Liu Z G. Some inverse relations and theta function identities. Int. J. Number Theory, 2012, 8: 1977-2002
[21]	Montaldi E, Zucchelli G. Additive decomposition for the product of two υ3 functions and modular equations. J. Math. Phys., 1989, 30: 2012-2015
[22]	Murayama T. On an identity of theta functions obtained from weight enumerators of linear codes. Proc. Japan Acad., Ser. A, 1998, 74: 98-100
[23]	Ono K. On the circular summation of the eleventh powers of Ramanujan's theta function. J. Number Theory, 1999, 76: 62-65
[24]	Rangachari S S. On a result of Ramanujan on theta functions. J. Number Theory, 1994, 48: 364-372
[25]	Shen L C. On the additive formula of the theta functions and a collection of Lambert series pertaining to the modular equations of degree 5. Trans. Amer. Math. Soc., 1994, 345: 323-345
[26]	Son S H. Circular summation of theta functions in Ramanujan's Lost Notebook. Ramanujan J., 2004, 8: 235-272
[27]	Xu P. An elementary proof of Ramanujan's circular summation formula and its generalizations. Ramanujan J., 2012, 27: 409-417