By Kenji Nagasaka

ISBN-10: 9810214995

ISBN-13: 9789810214999

Those lawsuits encompass invited papers by way of mathematicians reviewing the new growth in analytic quantity concept and similar issues. Papers on Diophantine approximations, zeta features, Dirichlet L-functions, common numbers, dispersion of multidimensional sequences, and Diophantine equations also are provided.

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**Extra resources for Analytic Number Theory & Related Topics Japan 11-13 November 1991**

**Sample text**

If an element j in KL is algebraic over k(~), then I( over k(t). (cf. 3} Corollary 2. Let f, g be elements in KL and algebraic over algebraic. k(~). Th The following is an advantage of considering the extended forma rings. Recall that the diagonal map is not defined on Q(k[W]). Corollary 3. Let f be an element of K and algebraic over k(~) th algebraic over k(t). Remark 3. The quantitative results in the paper8 are also vali form. Leinartas introduced generalized Hadamard products 10 • Let f g( 11) = E b(p.

1 Remark. The above theorem and cororally have some properties of multiple gamma function. 4 . The generalized Dedekind sum Let k1 , ... , be nonnegative integers, P = (p>, ... ,) a gral matrix, and z E R"'. ,. It follows from Proposition 1 an that for v = 1, ... ,(n-ll)(k 1, ... ,,. p , z )Qkt1 . • . , , and for a nonnegative integer JJ where Qi =

Tokyo24(1977),167-199. 9. D. Zagier,Higher dimensional Dedekind sums, Math. An ,149-172. This page is intentionally left blank Takasbi Harase Department of Mathematics, Tokyo Institute of Technolog Oh-okayama, Meguro-ku, Tokyo 152, Japan ABSTRACT The definition of extended formal power series rings and generalizations o results are given. o. Introduction. The elements of the fraction field of a formal powe single indeterminate over a field k are also expressed as formal pow finitely many negative exponents.

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