Number Theory, Analysis and Geometry

1. Front Matter

   Pages i-xx

   PDF

2. Raynaud’s group-scheme and reduction of coverings

   • Dan Abramovich, Jonathan Lubin

   Pages 1-18

3. The modular degree, congruence primes, and multiplicity one

   • Amod Agashe, Kenneth A. Ribet, William A. Stein

   Pages 19-49

4. Le théorème de Siegel–Shidlovsky revisité

   • Daniel Bertrand

   Pages 51-67

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

   • Eliot Brenner, Andrew Sinton

   Pages 69-109

6. Differential characters on curves

   • Alexandru Buium

   Pages 111-123

7. Weyl group multiple Dirichlet series of type A ₂

   • Gautam Chinta, Paul E. Gunnells

   Pages 125-142

8. On the geometry of the diffeomorphism group of the circle

   • Adrian Constantin, Boris Kolev

   Pages 143-160

9. Harmonic representatives for cuspidal cohomology classes

   • Józef Dodziuk, Jeffrey McGowan, Peter Perry

   Pages 161-168

10. About the ABC Conjecture and an alternative

    • Machiel van Frankenhuijsen

    Pages 169-180

11. Unifying themes suggested by Belyi’s Theorem

    • Wushi Goldring

    Pages 181-214

12. On the local divisibility of Heegner points

    • Benedict H. Gross, James A. Parson

    Pages 215-241

13. Uniform estimates for primitive divisors in elliptic divisibility sequences

    • Patrick Ingram, Joseph H. Silverman

    Pages 243-271

14. The heat kernel, theta inversion and zetas on Г∖G∕K

    • Jay Jorgenson, Serge Lang

    Pages 273-306

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

    • Anders Karlsson

    Pages 307-320

16. Report on the irreducibility of L-functions

    • Nicholas M. Katz

    Pages 321-353

17. Remark on fundamental groups and effective Diophantine methods for hyperbolic curves

    • Minhyong Kim

    Pages 355-368

18. Ranks of elliptic curves in cubic extensions

    • Hershy Kisilevsky

    Pages 369-383

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

    • D. Y. Kleinbock, G. A. Margulis

    Pages 385-396

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

    • Jürg Kramer, Anna-Maria von Pippich

    Pages 397-435

Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas of the field, namely Number Theory, Analysis, and Geometry, representing Lang’s own breadth of interest and impact. A special introduction by John Tate includes a brief and fascinating account of the Serge Lang’s life. This volume's group of 6 editors are also highly prominent mathematicians and were close to Serge Lang, both academically and personally. The volume is suitable to research mathematicians in the areas of Number Theory, Analysis, and Geometry.

• Bessel integrals
• Diophantine approximation
• Gelfand's transcendence criterion
• Lang-Trotter conjecture
• arithmetic dimension
• elliptic Einstein series
• elliptic divisibility sequence
• irreducibility of L-functions
• quadratic reciprocity

• , Department of Mathematics, Columbia University, New York, USA

  Dorian Goldfeld

• , Department of Mathematics, City College of New York, New York, USA

  Jay Jorgenson

• , Department of Mathematics, Yale University, New Haven, USA

  Peter Jones

• , Department of Mathematics, California Institute of Technology, Pasadena, USA

  Dinakar Ramakrishnan

• , Department of Mathematics, University of California at Berkeley, Berkeley, USA

  Kenneth Ribet

• , Department of Mathematics, Harvard University, Cambridge, USA

  John Tate

Policies and ethics