- E-mail Address:
- iwao@sci.u-toyama.ac.jp
- PGP
- Fingerprint20 = C077 88F2 AD67 4273 F92E 2962 63CC C32F 1169 F0AC
- Public Key,
- His address:
- Dept. of Mathematics, Faculty of Science, Toyama University, Toyama 930--8555, Japan.
- Telephone and Fax.
- tel:+81-764-45-6572 (Dept. Math.), fax:+81-764-45-6573.

My research interests are, roughly, study of number fields and of function fields of one variable over finite constant fields. Specifically, once we fix one such field F and rational prime l, we consider some families of quadratic extensions over F, for example, the set of quadratic extensions over F whose (relative) class numbers are not divisible by l.

The case that F is a totally real, l = 3 and the set of totally imaginary quadratic extensions over F is treated in Horie-Kimura 1999. This consideration also applied to the function field case, Kimura 1998.

I studied similar problems for imaginary quadratic fields and general l, related to recent progress made by Kohnen-Ono, Byeon and others (Kimura 2003).

I am now interested in similar problems, replacing class numbers of quadratic fields by orders of certain cohomology groups (algebraic K-groups) associated to rings of quadratic fields (Kimura MJTU 2003, Demonstratio Math., to appear).

- I. Kimura, Indivisibility of special values of zeta functions associated to real quadratic fields, submitted, 2007.
- I. Kimura, Divisibility of orders of K
_{2}groups associated to quadratic fields, Demonstratio Math., 39, 2006(2), pp.~277--284 - I. Kimura, Some implications of indivisibility of special values of zeta functions of real quadratic fields, Math. J. Toyama Univ., 26, 2003, 85--91.
- I. Kimura, A note on the existence of certain infinite families of imaginary quadratic fields, Acta Arith. 110(1), 2003, 37--43. Correction.
- On the densities and the mean three-class-numbers of quadratic extensions of number fields, in preparation.
- On the relative 3-class numbers of quadratic extensions of number fields and relative Iwasawa invariants of CM-fields.(In Japanese), Short communication at The Mathematical Society of Japan, Autumn 1995.
- "On the relative 3-class-numbers of quadratic extensions over number fields and relative Iwasawa invariants". Talk at Cooperative Research Conference "Algebraic Number Theory and Fermat's Problem" (organizer: Professor Keiichi Komatsu (J-TAGT)) at Research Institute for Mathematical Sciences (RIMS) 12/11-15.
- There is the draft for RIMS kokyuroku 971, proceedings for the above conference. (Sorry, in Japanese).
- K. Horie and I. Kimura, On quadratic extensions of number fields and Iwasawa invariants for basic Z
_{3}-extensions, J. Math. Soc. Japan 51(2), 1999, 387--402. - "On class numbers of quadratic extensions over function fields of finite constant fields", Short communication at The Mathematical Society of Japan, March 1997.
- I. Kimura, On class numbers of quadratic extensions over function fields, manuscripta mathematica, 97(1), 81--91, 1998. Dvi file, PostScript file and PDF file are available.
- I. KIMURA, There exist infinitely many imaginary quadratic function fields whose class number is not divisible by given prime other than characteristic (In Japanese), Short communication at The Mathematical Society of Japan, Oct, 1998 at Osaka University.

- I am using the following TeX environment for writing mathematics: AUC-TeX.

- There is a memo for how to compile PARI-GP in FreeBSD 2.1.5R box (sorry, in Japanese).
- There also is a memo for how to install pari-gp in Sun box.

- Online search for Math. Reviews. <-One needs to be a subscriber.
- American Mathematical Society (AMS) e-MATH Server
- The Electronic Publications of the AMS:- The Bulletin, Journal, Proceedings, and Transactions etc.
- Preprints concerning algebraic number theory.

- K. Matthews' Number Theory Web: Many number theory and number theorist related pages.
- The elliptic curves virtual study group. This group works with Silverman's
*Advanced Topics in the Arithmetic of Elliptic Curves*. - Virtual Study Group for "Automorphic Forms and Representaions" by D. Bump.
- "Tools for Number Theory": Math. Dept. of Tokyo Metropolitan University Top page.
- TNT ftp server in Dept. of Math, Osaka Univ.

- Facl. of Math, Toyama Univ. Home page
- Inst. of Math., University of Tsukuba Top Page
- University of Tsukuba Top Page

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My hearty thanks to Keith Matthews (krm@maths.uq.oz.au) for his help with my English.

Iwao KIMURA (iwao@sci.toyama-u.ac.jp)