Titlebook: Number Theoretic Methods; Future Trends Shigeru Kanemitsu,Chaohua Jia Book 2002 Springer Science+Business Media Dordrecht 2002 Algebra.Arit

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Some Aspects of Interactions between Algebraic Number Theory and Analytic Number Theory,This work is a historical exposition of mathematical ideas, methods and research programs which supported the birth and growth of modern Algebraic Number Theory. The mathematicians picked up here are Cardano, Fermat, Euler, Lagrange, Legendre, Gauss, Abel, Dirichlet, Kummer, Kronecker, Dedekind, Weber and Zolotareff.

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ALIAS

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A Historical Comment about the GVT in Short Interval,In this article, the author introduces the history, progress and method in the Goldbach-Vinogradov Theorem in short interval by which every sufficiently large odd integer could be expressed as the sum of three almost equal prime numbers.

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Developments in Mathematicshttp://image.papertrans.cn/n/image/668839.jpg

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https://doi.org/10.1007/978-1-4757-3675-5Algebra; Arithmetic; Finite; Identity; Prime; equation; function; mathematics; number theory; theorem

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,Infinite Sums, Diophantine Equations and Fermat’s Last Theorem,f Wiles: .... The modularity of elliptic curves over . is the content of the Shimura-Taniyama conjecture, and in this lecture, we will restrain ourselves to explaining in elementary terms the meaning of this deep conjecture.

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Zeta-Functions Defined by Two Polynomials,ed by two polynomials . and ., follows. Then the holomorphy of .(.; ., .) at non-positive integers is proved, and explicit formulas for the values .(0; ., .) and .(0; ., .) are given. The latter formula gives a generalization of an explicit formula for the regularized determinant of the Laplacian on the high-dimensional sphere.

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A Penultimate Step toward Cubic Theta-Weyl Sums,his paper we shall present basic ingredients for interpreting cubic Weyl sums as finite theta series, i.e. the cubic continued fraction expansion, the van der Corput reciprocal function, cubic reciprocal and parabolic transformations.