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Small Representations by Indefinite Ternary Quadratic Forms

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Number Theory and Related Fields

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 43))

Abstract

We study nonhomogeneous Pythagorean triples, that is, solutions of the diophantine equation \({x}^{2} + {y}^{2} - {z}^{2} = D\) where D is fixed and non-zero. We are particularly concerned, for D large and positive, with counting the solutions having x, y, z, all small relative to D.

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References

  1. W. Duke, J.B. Friedlander, H. Iwaniec, Weyl sums for quadratic roots, IMRN (2011)

    Google Scholar 

  2. W. Duke, R. Schulze-Pillot, Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids. Invent. Math. 99, 49–57 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  3. S.-C. Liu, R. Masri, The average of the divisor function over values of a quadratic polynomial (2012, preprint)

    Google Scholar 

  4. P. Michel, A. Venkatesh, Equidistribution, L-functions and ergodic theory: on some problems of Yu. V. Linnik, in Proc. ICM, vol II, Zurich, 2006, pp. 421–457

    Google Scholar 

  5. P. Michel, A. Venkatesh, The subconvexity problems for GL 2. Pub. Math. IHES 111, 171–271 (2010)

    MathSciNet  Google Scholar 

  6. N. Templier, J. Tsimerman, Non-split sums of coefficients of GL(2)-automorphic forms. Israel J. Math. (2013, in press)

    Google Scholar 

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Acknowledgements

JF was supported in part by NSERC grant A5123; HI was supported in part by NSF grant DMS-1101574.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, ON, Canada, M5S 2E4

    J. B. Friedlander

  2. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08903, USA

    H. Iwaniec

Authors
  1. J. B. Friedlander
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  2. H. Iwaniec
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Corresponding author

Correspondence to J. B. Friedlander .

Editor information

Editors and Affiliations

  1. , School of Math. & Physical Sciences, University of Newcastle, Callaghan, 2308, Australia

    Jonathan M. Borwein

  2. , Department of Computing, Macquarie University, Herring Road, North Ryde, 2109, New South Wales, Australia

    Igor Shparlinski

  3. , School of Math. & Physical Sciences, University of Newcastle, Callaghan, 2308, Australia

    Wadim Zudilin

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Friedlander, J.B., Iwaniec, H. (2013). Small Representations by Indefinite Ternary Quadratic Forms. In: Borwein, J., Shparlinski, I., Zudilin, W. (eds) Number Theory and Related Fields. Springer Proceedings in Mathematics & Statistics, vol 43. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6642-0_7

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