## Selected Papers on Number Theory and Algebraic GeometryThis book presents papers that originally appeared in the Japanese journal Sugaku from the Mathematical Society of Japan. The papers explore the relationship between number theory and algebraic geometry. |

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### Contents

Mahler Functions and Transcendental Numbers | 21 |

Recent Topics on Open Algebraic Surfaces | 61 |

Recent Topics on Toric Varieties | 77 |

### Common terms and phrases

abelian extensions adic field affine surface algebraic geometry algebraic number field algebraic surface algebraically independent class field theory coefficients complete discrete valuation complex numbers complex power conjecture convex bodies coordinate ring corresponding defined Denef denote Dieck dimensional discrete valuation field divisor dual duality element example Fano polytope finite field following theorem formula function field functional equation Gal(L/A Galois geometry of convex global field Hence higher-dimensional homology plane homomorphism hypersurface idele class group integer isomorphic Kodaira dimension linear local zeta function logarithmic Mahler functions Mathematics Milnor Miyanishi natural number Nishioka nonsingular number theory open algebraic surface p-adic Papers polynomial power series prehomogeneous vector spaces preprint prime ideal prime number problem proof proved Q-homology ramification rational function residue field resp Saito satisfies scheme SF(A sheaf singular point subgroup subset topological toric geometry toric varieties transcendental number UCL(A Univ variables Z-module zeta functions