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

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chastise

Calculus

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施舍

裹住

Partitions Modulo Prime Powers and Binomial Coefficients,In this paper, we show some identities which connect binomial coefficients with the number of solutions of congruences of some type.

沙發(fā)

,On the Nature of the “Explicit Formulas” in Analytic Number Theory — A Simple Example,We interpret the “explicit formulas” in the sense of analytic number theory for the zeta function of an elliptic curve over a finite field as a transversal index theorem on a 3-dimensional laminated space.

STANT

Product Representations by Rationals,A survey is made of the representability of arbitrary rationals by products of given rationals and their reciprocals. Rationals of number theoretic interest are emphasised. There are connections with group theory, harmonic analysis and the theory of algorithms. Outstanding problems of the discipline are identified.

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On the Distribution of , Modulo One,In this article, some topics on the approximation to the real number by rational numbers are introduced. In particular, the author introduces the progress on the situation in which the denominators of rational numbers are prime numbers and describes some methods used.

intercede

,Waldspurger’s Formula and Central Critical Values of ,-Functions of Newforms in Weight Aspect,We shall give a proof of the Lindel?f hypothesis in weight aspect on the average for central critical values of quadratic character twists of Hecke .-functions attached to cuspidal Hecke eigenforms. One of the basic tools will be Waldspurger’s results on central critical values of .-functions in weight aspect.