Number Theory: Arithmetic in Shangri-La

This volume is based on the successful 6th China–Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in their respective fields. The topics range from traditional analytic number theory — additive problems, divisor problems, Diophantine equations — to elliptic curves and automorphic L-functions. It contains new developments in number theory and the topics complement the existing two volumes from the previous seminars which can be found in the same book series.

Contents:

• On Jacobi Forms with Levels (Hiroki Aoki)
• Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review (Jörg Brüdern, Koichi Kawada and Trevor D Wooley)
• Annexe to the Gallery: An Addendum to “Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review” (Jörg Brüdern, Koichi Kawada and Trevor D Wooley)
• A Note on the Distribution of Primes in Arithmetic Progressions (Zhen Cui and Boqing Xue)
• Matrices of Finite Abelian Groups, Finite Fourier Transform and Codes (Shigeru Kanemitsu and Michel Waldschmidt)
• A Remark on a Result of Eichler (Yoshiyuki Kitaoka)
• On Weyl Sums over Primes in Short Intervals (Angel V Kumchev)
• On Congruences for Certain Binomial Coefficients of E Lehmer's Type (Takako Kuzumaki and Jerzy Urbanowicz)
• Sign Changes of the Coefficients of Automorphic L-Functions (Yuk-Kam Lau, Jianya Liu and Jie Wu)
• On Fourier Coefficients of Automorphic Forms (Guangshi Lü)
• The Twists of Hessian Elliptic Curves over Splitting Fields of Cubic Polynomials and the Related Elliptic 3-Folds (Katsuya Miyake)
• Asymptotic Voronoi's Summation Formulas and Their Duality for SL3(ℤ) (Xiumin Ren and Yangbo Ye)
• Jerzy Urbanowicz's Work in Pure Mathematics (Andrzej Schinzel)
• Conjectures Involving Arithmetical Sequences (Zhi-Wei Sun)

Readership: Graduate students and researchers in number theory.