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Number theory and related areas. (English) Zbl 1270.11002

Advanced Lectures in Mathematics (ALM) 27. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-273-2/pbk). 240 p. (2013).

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The papers comprising this volume explore various fields of number theory, including: the congruent property of solutions of quadratic Diophantine equations, \(K\)-groups over the ring of integers of number fields, \(L\)-functions of global function fields, automorphic forms, \(p\)-adic representations, and more. Applications of number theory, as in design and coding theory, are also explored. The research found in this volume can be seen as a reflection of the influence of Professor Keqin Feng upon the development of number theory studies in China, and this volume is therefore dedicated to him.
This collection is a valuable reference for experts in these fields, as well as an excellent introduction for graduate students.
The articles of this volume will be reviewed individually.
Indexed articles:
Ding, Cunsheng; Si, Wenpei, Binary additive counter stream ciphers, 1-23 [Zbl 1317.94102]
Feng, Tao; Wen, Bin; Xiang, Qing; Yin, Jianxing, Partial difference sets from quadratic forms and \(p\)-ary weakly regular bent functions, 25-40 [Zbl 1317.05192]
Guo, Xuejun; Qin, Hourong, Governing fields of the 4-rank of \(K_2\mathcal O_{\mathbb Q(\sqrt{dp})}\) as \(p\) varies, 41-50 [Zbl 1317.11119]
Han, Wenbao; Liu, Xianghui; Zeng, Guang; Tan, Gangmin, Word-oriented linear feedback shift registers: \(\sigma\)-LFSRs, 51-71 [Zbl 1317.94075]
Li, Wen-Ching Winnie; Xiong, Maosheng, Statistics of zeros of families of \(L\)-functions over function fields: a survey, 73-84 [Zbl 1317.11066]
Ouyang, Yi, Lectures on \(p\)-adic zeta functions and \((\phi,\Gamma)\)-modules, 85-147 [Zbl 1320.11113]
Sun, Zhi-Wei, Conjectures and results on \(x^2\pmod p^2\) with \(4p=x^2+dy^2\), 149-197 [Zbl 1317.11034]
Yang, Tonghai, Harmonic weak Maass forms, automorphic Green functions and period integrals, 199-223 [Zbl 1317.11062]
Ye, Yu; Zhang, Pu, Some recent progress in higher Koszulity., 225-240 [Zbl 1317.16026]

MSC:

11-06 Proceedings, conferences, collections, etc. pertaining to number theory
00B15 Collections of articles of miscellaneous specific interest
05-06 Proceedings, conferences, collections, etc. pertaining to combinatorics
14-06 Proceedings, conferences, collections, etc. pertaining to algebraic geometry
16-06 Proceedings, conferences, collections, etc. pertaining to associative rings and algebras
94-06 Proceedings, conferences, collections, etc. pertaining to information and communication theory
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