Book 2012

Number Theory, Analysis and Geometry

In Memory of Serge Lang

ISBN: 978-1-4614-1259-5 (Print) 978-1-4614-1260-1 (Online)

Table of contents (29 chapters)

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  1. Front Matter

    Pages i-xx

  2. Chapter

    Pages 1-18

    Raynaud’s group-scheme and reduction of coverings

  3. Chapter

    Pages 19-49

    The modular degree, congruence primes, and multiplicity one

  4. Chapter

    Pages 51-67

    Le théorème de Siegel–Shidlovsky revisité

  5. Chapter

    Pages 69-109

    Some aspects of harmonic analysis on locally symmetric spaces related to real-form embeddings

  6. Chapter

    Pages 111-123

    Differential characters on curves

  7. Chapter

    Pages 125-142

    Weyl group multiple Dirichlet series of type A 2

  8. Chapter

    Pages 143-160

    On the geometry of the diffeomorphism group of the circle

  9. Chapter

    Pages 161-168

    Harmonic representatives for cuspidal cohomology classes

  10. Chapter

    Pages 169-180

    About the ABC Conjecture and an alternative

  11. Chapter

    Pages 181-214

    Unifying themes suggested by Belyi’s Theorem

  12. Chapter

    Pages 215-241

    On the local divisibility of Heegner points

  13. Chapter

    Pages 243-271

    Uniform estimates for primitive divisors in elliptic divisibility sequences

  14. Chapter

    Pages 273-306

    The heat kernel, theta inversion and zetas on Г∖GK

  15. Chapter

    Pages 307-320

    Applications of heat kernels on abelian groups: ζ(2n), quadratic reciprocity, Bessel integrals

  16. Chapter

    Pages 321-353

    Report on the irreducibility of L-functions

  17. Chapter

    Pages 355-368

    Remark on fundamental groups and effective Diophantine methods for hyperbolic curves

  18. Chapter

    Pages 369-383

    Ranks of elliptic curves in cubic extensions

  19. Chapter

    Pages 385-396

    On effective equidistribution of expanding translates of certain orbits in the space of lattices

  20. Chapter

    Pages 397-435

    Elliptic Eisenstein series for \({PSL}_{2}(\mathbb{Z})\)

  21. Chapter

    Pages 437-459

    Consequences of the Gross–Zagier formulae: Stability of average L-values, subconvexity, and non-vanishing mod p

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