Number Theory, Analysis and Geometry

Table of Contents

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   Book Overview
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   Chapter 1 Raynaud’s group-scheme and reduction of coverings
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   Chapter 2 The modular degree, congruence primes, and multiplicity one
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   Chapter 3 Le théorème de Siegel–Shidlovsky revisité
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   Chapter 4 Some aspects of harmonic analysis on locally symmetric spaces related to real-form embeddings
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   Chapter 5 Differential characters on curves
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   Chapter 6 Weyl group multiple Dirichlet series of type A 2
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   Chapter 7 On the geometry of the diffeomorphism group of the circle
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   Chapter 8 Harmonic representatives for cuspidal cohomology classes
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    Chapter 9 About the ABC Conjecture and an alternative
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    Chapter 10 Unifying themes suggested by Belyi’s Theorem
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    Chapter 11 On the local divisibility of Heegner points
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    Chapter 12 Uniform estimates for primitive divisors in elliptic divisibility sequences
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    Chapter 13 The heat kernel, theta inversion and zetas on Г∖ G ∕ K
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    Chapter 14 Applications of heat kernels on abelian groups: ζ(2 n ), quadratic reciprocity, Bessel integrals
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    Chapter 15 Report on the irreducibility of L -functions
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    Chapter 16 Remark on fundamental groups and effective Diophantine methods for hyperbolic curves
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    Chapter 17 Ranks of elliptic curves in cubic extensions
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    Chapter 18 On effective equidistribution of expanding translates of certain orbits in the space of lattices
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    Chapter 19 Elliptic Eisenstein series for $${PSL}_{2}(\mathbb{Z})$$
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    Chapter 20 Consequences of the Gross–Zagier formulae: Stability of average L -values, subconvexity, and non-vanishing mod p
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    Chapter 21 A variant of the Lang–Trotter conjecture
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    Chapter 22 Multiplicity estimates, interpolation, and transcendence theory
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    Chapter 23 Sampling spaces and arithmetic dimension
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    Chapter 24 Recovering function fields from their decomposition graphs
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    Chapter 25 Irreducible spaces of modular units
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    Chapter 26 Equidistribution and generalized Mahler measures
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    Chapter 27 Représentations p -adiques de torsion admissibles
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    Chapter 28 Multiplier ideal sheaves, Nevanlinna theory, and Diophantine approximation
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    Chapter 29 Recent advances in Diophantine approximation