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Analytic Number Theory & Related Topics Japan 11-13 November by Kenji Nagasaka

By Kenji Nagasaka

Those lawsuits encompass invited papers by means of mathematicians reviewing the hot growth in analytic quantity idea and comparable subject matters. Papers on Diophantine approximations, zeta services, Dirichlet L-functions, general numbers, dispersion of multidimensional sequences, and Diophantine equations also are awarded.

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Cr(z) = f3o,rZo + · · · + f3d,rZd independantes a coefficients dans Q, sur l'espace tangent Tg 1 :5 i :5 k, soit u; E Ta;(C),u; f. 0 tel que 'Yi = expa;(u;) ap Soit K le corps engendre sur K 0 par tous les coefficients de n et toutes les coordonnees projectives des 'Yb · · · ,'"fk· Dans §3(4 f3I. Cr(1 :5 T :5 t), et on considere une {'7I = 1, '72• · · · , '7D} formee d'elements de }'ensemble a -t Notons c5 le degre de K 0 sur Q. Soit {(t. v} une base de K sur Q formee d'elements {r1i(;;1 j ::; c5 }.

I be a nonzero element assumption of (2) there is an unique monomial ~!.. which has L(~) in the monomials in f with nonzero coefficients. g where g = 1 + h with h = ~L(i)>o a(i. + io) g' = 1 + (-h) 1 + (-h) 2 + ... is L- finite and the inverse of g, so f has Remark 1. Under the assumptions a;> 0 (i = 1, ... ,m), KL Q(k[(x~>···•xm]]). ···,xm]]) is contained in the smal in which all exponents of each element are contained in some c respectively. (cf. ·!! 2. Let ~ = (6, ... ,= ("'t, ... , "'m) be respectively nand m-tup terminates respectively, and let A= (a;,i) be an (m,n) matrix wit ai,i· We use the following notation Then it is clear that ~~'A= (~A)~' for integer vector p = (p1, ...

Halbritter and M. Pohst, On the computation of the v functions of totally real cubic fields, J. Number Th. 36(199 7. H. Rademacher and E. l6,( Mathematical Association of America, D. C. ,1973). 8. T. Shintani, On a Kronecher limit formula for real quadratic Sci. Univ. 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.

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