Diophantine Analysis and Related Fields 2006
in honor of Prof. Iekata SHIOKAWA• Dates: 7–10 March, 2006
• Place: Large Conference Room on the 2nd floor, Raio-sha Building (indicated as No.10;
a route from Hiyoshi Station), Hiyoshi Campus, Keio University, Yokohama, JAPAN• Accommodation: Hotel Aurora (attached to Kawasaki International Center)• Organizers: M. Katsurada (Keio Univ.); T. Komatsu (Hirosaki Univ.)• Contact: katsurad ＠ hc.cc.keio.ac.jp; komatsu ＠ cc.hirosaki-u.ac.jp

Conference background and scope:
The conference on Diophantine Analysis and Related Fields 2006 will take place, whichis sponsored by Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research, Nos. 1554021; 16540038), by Keio University (Academic Research Promotion Fundsand Economics Faculty Fund), as well as by Fund for the Promotion of International Scientific Research (Grant B-1, 2005). The conference aims to report recent progress anddevelopments of diophantine aspects of analytic number theory, especially focusing upon
the topics in diophantine analysis and related fields; its simultaneous objectives are to promote interactions between analytic number theorists and mathematicians from other fields,
and further to create opportunities for opening up new individual/collaborative research
projects. The conference will be held in honor of Professor Iekata Shiokawa on the occasionof his retirement from Keio University.

Program:
Tuesday 7 March
12:55–13:00

Opening

13:00–14:00

Igor Shparlinski (Macquarie Univ.),
William Banks (Univ. Missouri)
Character sums with Beatty sequences

14:30–15:10

Florian Luca (Inst. de Mat. UNAM),
On the irrationality of a certain series

15:30–16:10

Takaaki Tanaka (Keio Univ.)
Algebraic independence of a certain series and its
subseries with subscripts in a geometric progression

16:40–17:10

Carsten Elsner (Univ. Hannover)New series transformations for Euler’s constant

17:30–18:00

Isao Wakabayashi (Seikei Univ.)
Cubic Thue equations with automorphisms

1/3

Wednesday 8 March
10:00–11:00

Matthias Beck (San Francisco State Univ.)
Dedekind sums: a geometric viewpoint

11:30–12:30

Michel Waldschmidt (Univ. Pierre et Marie Curie)
Diophantine analysis and words

14:00–15:00

Carsten Elsner (Univ. Hannover),Shun Shimomura and Iekata Shiokawa (Keio Univ.)
Explicit algebraic relations for reciprocal sums of evenpowers of Fibonacci numbers

15:30–16:30

Ryotaro Okazaki (Doshisha Univ.)
Numbers of solutions to simultaneous Pell equations ofindefinite signature

17:00–17:30

Yuzen Tanaka (Chiba Univ.)
Rational approximation of (1 + x)a and applications toThue inequalities

18:00–20:00

Reception Party at Faculty Lounge

Thursday 9 March
10:00–11:00

Douglas Bowman (Northern Illinois Univ.)
James McLaughlin (West Chester Univ.)
Limit sets for infinite matrix products and continued
fractions

11:30–12:30

Yuri Nesterenko (Moscow State Univ.)
Algebraic independence in the p-adic domain14:00–15:00

Hitoshi Nakada (Keio Univ.)
On the metric theory of continued fractions

15:30–16:30

Takao Komatsu (Hirosaki Univ.)
More on Hurwitz and Tasoev continued fractions

17:00–18:00

Khrystyna Kuchmins’ka (Lviv Polytechnic National Univ.)
Multidimensional generalization of continued fractions:
history, main results, new senture problems

2/3

Friday 10 March
10:00–11:00

Yohei Tachiya (Keio Univ.)
Equivalent conditions for the algebraicity of the values ofcertain infinite products

11:15–11:45

Zenji Kobayashi (Tohoku Gakuin Univ.),
Tatsuya Okada (Fukushima Pref. Med. Univ.),
Takeshi Sekiguchi and Yasunobu Shioda (Tohoku Gakuin Univ.)
Applications of measure theory to digital sum problems

11:55–12:25

David Adam (Univ. Amiens and Nihon Univ.)
On integer-valued functions in positive characteristic

12:25–12:30

ClosingTime table
Mar. 7 (Tue.)

12:55–13:00
Opening
13:00–14:00
I. Shparlinski
14:30–15:10
F. Luca
15:30–16:10
Ta. Tanaka
16:30–17:10
C. Elsner
17:30–18:00
I. Wakabayashi

Mar. 8 (Wed.)
10:00–11:00
M. Beck
11:30–12:30
M. Waldschmidt
12:30–14:00
Lunch break
14:00–15:00
I. Shiokawa
15:30–16:30
R. Okazaki
17:00–17:30
Yu. Tanaka
18:00–20:00
Reception party

3/3

Mar. 9 (Th.)
10:00–11:00
D. Bowman
11:30–12:30
Y. Nesterenko
12:30–14:00
Lunch break
14:00–15:00
H. Nakada
15:30–16:30
T. Komatsu
17:00–18:00
K. Kuchmins’ka

Mar. 10. (Fri.)
10:00–11:00
Y. Tachiya
11:15–11:45
Z. Kobayashi
11:55–12:25
D. Adam
12:25–12:30
Closing