Section 03  Number Theory and Arithmetic Algebraic Geometry

Section 03: Number Theory and Arithmetic Algebraic Geometry

Invited Lectures

Saturday, 22 August  MA 005

14:00 – 14:45 Vladimir Berkovich, Weizmann Institute of Science, Rehovot, Israel p-adic analytic spaces (I: p.48, electronic version) Chair: Norbert Schappacher

15:00 – 15:45 Pierre Colmez, CNRS, ENS, and Institut de Mathématiques de Jussieu, Paris, France (φ, Γ)-modules and Iwasawa theory of p-adic representations (I: p.49) Chair: Christophe Soulé

Monday, 24 August  MA 005

16:15 – 17:00 François Gramain, Université Jean Monnet Saint-Etienne, Saint-Etienne, France Some results of algebraic independence (I: p.51) Chair: Michel Waldschmidt

17:15 – 18:00 William Duke, Rutgers University, New Brunswick, USA Bounds for arithmetic multiplicities (I: p.50) Chair: Per Salberger

Tuesday, 25 August  MA 005

14:00 – 14:45 Loïc Merel, Université Paris 7 - Denis Diderot, Paris, France Determination of rational points using Dirichlet series (I: p.52) Chair: Wilhelm Zink

15:00 – 15:45 Shinichi Mochizuki, RIMS, Kyoto University, Kyoto, Japan The Intrinsic Hodge Theory of p-adic Hyperbolic Curves (I: p.53) Chair: Helmut Koch

Wednesday, 26 August  MA 005

15:00 – 15:45 Takeshi Tsuji, RIMS, Kyoto University, Kyoto, Japan p-adic Hodge Theory in the semi-stable reduction case (I: p.55) Chair: Helmut Koch

16:15 – 17:00 Shou-Wu Zhang, Columbia University, New York City, USA Small points, Heegner points, and Arakelov theory (I: p.57) Chair: Jürg Kramer

17:15 – 18:00 Hans Peter Schlickewei, Universität Marburg, Marburg, Germany The Absolute Subspace Theorem and Applications (I: p.54) Chair: Alfred J. van der Poorten

Number Theory and Arithmetic Algebraic Geometry  Section 03

Short Communications and Poster Sessions

Short Communications  Wednesday, 19 August
Computational Number Theory  MA 311

Chair: Michael E. Pohst

14:00 – 14:15 Claus Fieker, Technische Universität Berlin, Berlin, Germany On Constructive Class Field Theory (p.36)

14:15 – 14:30 István Gaál, KLTE, Institute of Mathematics, Debrecen, Hungary Power integral bases in algebraic number fields (p.36)

14:30 – 14:45 Jürgen Klüners, Universität Heidelberg, Heidelberg, Germany Explicit Galois realization of transitive groups of degree up to 15 (p.40)

Additive Number Theory  MA 311

Chair: Doytchin Tolev

15:00 – 15:15 Mariano Garcia, Touro College, N.Y. City, USA New type (i, 1) amicable pairs with greatest common factor a power of 2 or a prime times a power of 2 (p.37)

15:15 – 15:30 Nazir M. Khan, GIK Institute of Engg. Sc. & Tech., Topi-Swabi, Pakistan The Numbers that Can Be Represented as the Sum of Four Squares (One Repeating Itself Three Times), in Three Different Ways (p.39)

15:30 – 15:45 Doytchin Tolev, University of Plovdiv, Plovdiv, Bulgaria Additive problem with prime numbers of a special type (p.46)

Short Communications  Thursday, 20 August
Cyclotomy  MA 311

Chair: Stanley J. Gurak

14:00 – 14:15 Grzegorz, M. Banaszak, Wydzial Matematyki i Informatyki, Univ., Poznan, Poland Wild kernel for higher K-groups and arithmetic of square rings (p.34)

14:15 – 14:30 Mónica del Pilar Canales, Universidad Austral de Chile, Valdivia, Chile Higher levels of Z/p^{l}Z and cyclotomy (p.34)

14:30 – 14:45 Stanley J. Gurak, University of San Diego, San Diego CA, USA On the factors Φ^{(jδ/m)}(x) of the period polynomial for finite fields (p.37)

Function Fields and Curves I  MA 311

Chair: Franck Leprévost

15:00 – 15:15 Florian Heß, TU Berlin, Berlin, Germany Effective construction of Riemann-Roch spaces in global function fields (p.38)

15:15 – 15:30 Ryutaro Horiuchi, Doshisha University, Kyotanabe-shi, Japan On Weierstrass Points of the Fermat Curve (p.38)

15:30 – 15:45 Franck Leprévost, Technische Universität Berlin, Berlin, Germany On some elliptic surfaces and elliptic curves related to discriminants of cubic or quartic polynomials

(p.41)

Short Communications  Friday, 21 August
Algebraic Geometry I  MA 311

Chair: Jürgen Wolfart

16:15 – 16:30 Emmanuel Peyre, Université de Strasbourg, Strasbourg, France Heights and Tamagawa measures (p.44)

16:30 – 16:45 Valentin E. Voskresenskii, Samara State University, Samara, Russia Stably rational algebraic tori (p.46)

16:45 – 17:00 Jürgen Wolfart, Universität Frankfurt, Frankfurt, Germany Riemann surfaces with many automorphisms (p.47)

Section 03  Number Theory and Arithmetic Algebraic Geometry

Modular Forms  MA 311

Chair: Yoichi Uetake

17:15 – 17:30 Werner Hoffmann, Institute for Advanced Study, Princeton NJ, USA Spectral estimates for noncompact quotients (p.38)

17:30 – 17:45 Wladimir de Azevedo Pribitkin, Max Planck Institute for Mathematics, Bonn, Germany Bol’s identity, fractional differentiation, and automorphic integrals (p.45)

17:45 – 18:00 Yoichi Uetake, Adam Mickiewicz University, Poznań, Poland A weak resolvent representation of a scattering matrix for automorphic functions (p.46)

Short Communications  Saturday, 22 August
Integral Matrices  MA 311

Chair: Jean-Louis Nicolas

16:15 – 16:30 Shashikant Katre, University of Pune, Pune, India Matrices over orders in algebraic number fields as sums of k-th powers (p.39)

16:30 – 16:45 Dmitri Malinin, Byelorussian State Pedagogical University, Minsk, Belarus Integral representations of finite groups (p.42)

16:45 – 17:00 Jean-Louis Nicolas, Universite Claude Bernard, Villeurbanne, France On the maximum order of torsion elements in GL(n, ℤ) (p.43)

Algebraic Geometry II  MA 042

Chair: Jörg Wildeshaus

16:15 – 16:30 Jörg Wildeshaus, Math. Inst. der Univ. Münster, Münster, Germany Degeneration of Shimura Polylogarithms

Analytic Number Theory I  MA 311

Chair: Jin Nakagawa

17:15 – 17:30 Antanas Laurincikas, Vilnius University, Vilnius, Lithuania Value-distribution theorems on Lerch zeta-functions (p.40)

17:30 – 17:45 Roberto J. Miatello, University Nac. Cordoba, Cordoba, Argentina Estimates for Kloosterman sums for totally real number fields (p.42)

17:45 – 18:00 Jin Nakagawa, Jeotsu University of Education, Joetsu, Japan Ohno conjecture on the zeta functions associated with the space of binary cubic forms (p.43)

Short Communications  Monday, 24 August
Lattices and Codes  MA 311

Chair: Fei Xu

14:00 – 14:15 San Ling, National University of Singapore, Singapore, Singapore Group algebras and codes (p.41)

14:15 – 14:30 Katherine S. Roegner, Technische Universität Berlin, Berlin, Germany Computing even, unimodular lattices with complete root systems (p.46)

14:30 – 14:45 Fei Xu, Mathematisches Institut Universität Münster, Münster, Germany Arithmetic Springer Theorem on Quadratic Forms under Field Extensions of Odd Degree (p.48)

Diophantine Problems  MA 311

Chair: Pieter Moree

15:00 – 15:15 Arturas Dubickas, Vilnius University, Vilnius, Lithuania Polynomials vanishing at 1 with high multiplicity and Tarry’s problem (p.35)

15:15 – 15:30 Florian G. Luca, Syracuse University, Syracuse NY, USA Equations Involving the Euler ϕ Function (p.42)

15:30 – 15:45 Pieter Moree, Max-Planck-Institut, Bonn, Germany Distribution of primes having a prescribed primitive root over residue classes (p.43)

Number Theory and Arithmetic Algebraic Geometry  Section 03

Short Communications  Tuesday, 25 August
Arithmetic Functions  MA 311

Chair: Yasutoshi Nomura

16:15 – 16:30 Philippe Ph. Elbaz-Vincent, CNRS, Montpellier, France On Poly(ana)logs (p.35)

16:30 – 16:45 Arne Winterhof, Institut für Algebra und Zahlentheorie, Braunschweig, Germany On Incomplete Character Sums (p.47)

16:45 – 17:00 Yasutoshi Nomura, Okayama University of Science, Okayama, Japan Arithmetic functions associated with arithmetic-geometric mean quotients (p.44)

Analytic Number Theory II  MA 311

Chair: Jan-Christoph Puchta

17:15 – 17:30 Julio Alcantara-Bode, PUCP, IMCA, Lima, Peru Reorderings of some divergent series and applications (p.34)

17:30 – 17:45 Michel L. Lapidus, University of California, Riverside, CA, USA Complex Dimensions of Fractal Strings and Oscillatory Phenomena in Fractal Geometry and Arithmetic (p.40)

17:45 – 18:00 Jan-Christoph Puchta, Budapest, Hungary Estimating Dirichlet L-serieses close to the line 1 + it (p.45)

Short Communications  Wednesday, 26 August
Function Fields and Curves II  MA 311

Chair: Dmitry Logachev

14:00 – 14:15 Sudhir R. Ghorpade, Indian Institute of Technology, Bombay, India Number of Points of Singular Varieties over Finite Fields (p.37)

14:15 – 14:30 Seman Wong, Brown University, Providence, Rhode Island, USA On the density of elliptic curves (p.47)

14:30 – 14:45 Dmitry Logachev, MIRAN Section of Algebra, Moscow, Russia Mazur–Bloch method for Siegel threefolds (p.41)

Poster Session  Thursday, 20 August 16:15 – 18:00  MA 144

Francis W. Clarke, University of Wales Swansea, Swansea, Great Britain

Closed formulas for representing primes by binary quadratic forms (p.35) Herbert Gangl, MPI für Mathematik, Bonn, Germany

Polylogarithmic identities in cubical higher Chow groups (p.36) Noriaki Kimura, Nihon University, Narashino, Japan

A simple proof of Carlitz’s congruence of Vandiver type (p.39) Tatsuya Okada, Fukushima Medical College, Fukushima, Japan

Explicit formulas for a generalized digital sum problem (p.44) Margaret M. Robinson, Mount Holyoke College, South Hadley, USA

Igusa local zeta functions (p.45)