On the theorem of Conrey and Iwaniec

Jeffrey Stopple
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 19, 2013, Number 2, Pages 1—9
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Authors and affiliations

Jeffrey Stopple
Department of Mathematics
University of California, Santa Barbara
Santa Barbara, CA 93106-3080

Abstract

An exposition on ‘Spacing of zeros of Hecke L-functions and the class number problem’ by Conrey and Iwaniec.

Keywords

  • Theorem of Conrey–Iwaniec
  • Quadratic form

AMS Classification

  • 11M20
  • 11R29

References

  1. Conrey, B., H. Iwaniec, Spacing of zeroes of Hecke L-functions and the class number problem, Acta Arith, Vol. 103, 2002, 259–312.
  2. Deuring, M. Zetafunktionen quadratischer Formen, J. Reine Angew. Math., Vol. 172, 1934, 226–252.
  3. Euler, L. De serie Lambertiana plurimisque eius insignibus proprietatibus, Opera Omnia Ser. 1, Vol. 6, 350–369.
  4. Firk, F. W. K., S. J. Miller, Nuclei, Primes and the Random Matrix Connection, Symmetry, Vol. 1, 2009, 64–105. http://dx.doi.org/10.3390/sym1010064
  5. Forrester, P., A. Odlyzko. A nonlinear equation and its application to nearest neighbor spacings for zeros of the zeta function and eigenvalues of random matrices. http://www.cecm.sfu.ca/organics/papers/odlyzko/nonlinear/ html/paper.html
  6. Gauss, C. Disquisitiones Arithmeticae (translated by Arthur A. Clarke), Yale University Press, 1966.
  7. Heath-Brown, R. Small Class Number and the Pair Correlation of Zeros, talk at the conference ‘In Celebration of the Centenary of the Proof of the Prime Number Theorem: A Symposium on the Riemann Hypothesis’ Seattle, 1996. Videotape: American Institute of Mathematics.
  8. Heilbronn, H. On the class number in imaginary quadratic fields, Quart. J. Math., Vol. 5, 1934, 150–160.
  9. Hopkins, K., J. Stopple, Lower bounds for the principal genus of definite binary quadratic forms, Integers, Vol. 10, 2010, 257–264.
  10. Montgomery, H. L., The pair correlation of zeros of the zeta function, Proceedings Symp. Pure Math., Vol. 24, 1972, 190–202.
  11. Montgomery, H. L., Corrélations dans l’ensemble des zéros de la fonction zêta, Séminaire de Théorie des Nombres, 1971–72 (Univ. Bordeaux I, Talence), Exp. No. 19.
  12. Oesterlé, J. Nombres de classes des corps quadratiques imaginaires, Sém. Bourbaki, Vol. 1983/84, Astérisque, No. 121–122, 1985, 309–323.
  13. Pólya, G., G. Szegö, Aufgaben und Lehrsätze der Analysis, Berlin, 1925. Reprinted as Problems and Theorems in Analysis I, Springer-Verlag, Berlin, 1998.
  14. Porter, C. E. Statistical Theories of Spectra: Fluctuations, Academic Press, 1965.
  15. Stark, H., On the tenth complex quadratic field with class number one, Ph.D. thesis, University of California, Berkeley, 1964.
  16. Stark, H., On the zeros of Epstein’s zeta function, Mathematika, Vol. 14, 1967, 47–55.
  17. Stopple, J. Notes on the Deuring-Heilbronn phenomenon, Notices Amer. Math. Soc., Vol. 53, 2006, 864–875. http://www.ams.org/notices/200608/fea-stopple.pdf
  18. Titchmarsh, E. C. The Theory of the Riemann Zeta Function, Oxford Press, 2nd ed., 1986.
  19. Watkins, M. Class numbers of imaginary quadratic fields, Ph.D. thesis, University of Georgia, 2000.
  20. Weinberger, P. Exponents of the class groups of complex quadratic fields, Acta Arith., Vol. XXII, 1973, 117–124.

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Cite this paper

APA

Stopple, J. (2013). On the theorem of Conrey and Iwaniec. Notes on Number Theory and Discrete Mathematics, 19(2), 1-9.

Chicago

Stopple, Jeffrey. “On the Theorem of Conrey and Iwaniec.” Notes on Number Theory and Discrete Mathematics 19, no. 2 (2013): 1-9.

MLA

Stopple, Jeffrey. “On the Theorem of Conrey and Iwaniec.” Notes on Number Theory and Discrete Mathematics 19.2 (2013): 1-9. Print.

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