The Michigan Mathematical Journal

Iterates of Vinogradov's quadric and prime paucity

Valentin Blomer and Jörg Brüdern

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Michigan Math. J., Volume 59, Issue 1 (2010), 231-240.

First available in Project Euclid: 27 April 2010

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Zentralblatt MATH identifier

Primary: 11N45: Asymptotic results on counting functions for algebraic and topological structures 11N36: Applications of sieve methods
Secondary: 11E25: Sums of squares and representations by other particular quadratic forms 11P32: Goldbach-type theorems; other additive questions involving primes


Blomer, Valentin; Brüdern, Jörg. Iterates of Vinogradov's quadric and prime paucity. Michigan Math. J. 59 (2010), no. 1, 231--240. doi:10.1307/mmj/1272376035.

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  • V. Blomer and J. Brüdern, Prime paucity for sums of two squares, Bull. London Math. Soc. 40 (2008), 457--462.
  • ------, A quadric with arithmetic paucity, Quart. J. Math. 60 (2009), 283--290.
  • ------, The number of integer points on Vinogradov's quadric, Monatsh. Math. (to appear).
  • V. Blomer and A. Granville, Estimates for representation numbers of quadratic forms, Duke Math. J. 135 (2006), 261--302.
  • P. Erdős, On additive properties of squares of primes, I, Proc. Acad. Wet. Amsterdam 41 (1938), 37--41.
  • I. S. Gradshteyn and I. M. Ryzhik, Tables of integrals, series, and products, 5th ed., Academic Press, Boston, 1994.
  • L. K. Hua, Introduction to number theory, Springer-Verlag, Berlin, 1982.
  • K. Prachar, Primzahlverteilung, Springer-Verlag, Berlin, 1957.
  • R. A. Rankin, Sums of powers of cusp form coefficients, Math. Ann. 263 (1983), 227--236.
  • G. J. Rieger, Über die Summe aus einem Quadrat und einem Primzahlquadrat, J. Reine Angew. Math. 231 (1968), 89--100.