# Number Theory

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*V. Kumar Murty; Michel Waldschmidt*

# Table of Contents

## Number Theory

- Contents v6 free
- Part I. Arithmetic Algebraic Geometry 110 free
- Relative splitting of one-motives 312
- The Hasse principle in a pencil of algebraic varieties 1928
- Stark-Heegner points over real quadratic fields 4150
- On the Hecke action on the cohomology of Hilbert-Blumenthal surfaces 7180
- The ABC conjecture and exponents of class groups of quadratic fields 8594
- Heights of points on subvarieties of Gnm 97106
- A note on a geometric analogue of Ankeny-Artin-Chowla's conjecture 101110

- Part II. Automorphic Forms 107116
- Determinant of representations of division algebras of prime degree over local fields 109118
- Mod p modular forms 135144
- On exceptions of integral quadratic forms 151160
- A brief survey on the theta correspondence 171180
- Deformations of Siegel-Hilbert Hecke eigensystems and their Galois representations 195204

- Part III. Elementary and Analytic Number Theory 227236
- A new key identity for Göllnitz' (Big) partition theorem 229238
- Some local-convexity theorems for the zeta-function-like analytic functions - III 243252
- Perfect powers in products of terms in an arithmetical progression IV 257266
- On some connections between probability and number theory 265274
- Inhomogeneous minima of a class of quaternary quadratic forms of type (2,2) 275284
- On an arithmetical inequality, II 299308

- Part IV. Transcendental Number Theory 303312
- Algebraic numbers close to 1: results and methods 305314
- Transcendence in positive characteristic 317326
- Minorations des hauteurs normalisées des sous-variétés de variétés abéliennes 333342
- Klein polygons and geometric diagrams 365374
- Sails and Klein polyhedra 373382
- Automata and transcendence 387396