The divisor problem for binary cubic forms

Tim Browning[1]

  • [1] School of Mathematics University of Bristol Bristol BS8 1TW United Kingdom

Journal de Théorie des Nombres de Bordeaux (2011)

  • Volume: 23, Issue: 3, page 579-602
  • ISSN: 1246-7405

Abstract

top
We investigate the average order of the divisor function at values of binary cubic forms that are reducible over ℚ and discuss some applications.

How to cite

top

Browning, Tim. "The divisor problem for binary cubic forms." Journal de Théorie des Nombres de Bordeaux 23.3 (2011): 579-602. <http://eudml.org/doc/219762>.

@article{Browning2011,
abstract = {We investigate the average order of the divisor function at values of binary cubic forms that are reducible over $\mathbb\{Q\}$ and discuss some applications.},
affiliation = {School of Mathematics University of Bristol Bristol BS8 1TW United Kingdom},
author = {Browning, Tim},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {divisor function; cubic form; linear factors; sum; ternary additive divisor problem},
language = {eng},
month = {11},
number = {3},
pages = {579-602},
publisher = {Société Arithmétique de Bordeaux},
title = {The divisor problem for binary cubic forms},
url = {http://eudml.org/doc/219762},
volume = {23},
year = {2011},
}

TY - JOUR
AU - Browning, Tim
TI - The divisor problem for binary cubic forms
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2011/11//
PB - Société Arithmétique de Bordeaux
VL - 23
IS - 3
SP - 579
EP - 602
AB - We investigate the average order of the divisor function at values of binary cubic forms that are reducible over $\mathbb{Q}$ and discuss some applications.
LA - eng
KW - divisor function; cubic form; linear factors; sum; ternary additive divisor problem
UR - http://eudml.org/doc/219762
ER -

References

top
  1. V. V. Batyrev and Yu. I. Manin, Sur le nombre des points rationnels de hauteur borné des variétés algébriques. Math. Ann. 286 (1990), 27–43. Zbl0679.14008MR1032922
  2. R. de la Bretèche and T. D. Browning, Binary linear forms as sums of two squares. Compositio Math. 144 (2008), 1375–1402. Zbl1234.11132MR2474314
  3. R. de la Bretèche and T. D. Browning, Le problème des diviseurs pour des formes binaires de degré 4 . J. reine angew. Math. 646 (2010), 1–44. Zbl1204.11158MR2719554
  4. S. Daniel, On the divisor-sum problem for binary forms. J. reine angew. Math. 507 (1999), 107–129. Zbl0913.11041MR1670278
  5. W. Duke, J. B. Friedlander and H. Iwaniec, A quadratic divisor problem. Inventiones Math. 115 (1994), 209–217. Zbl0791.11049MR1258903
  6. T. Estermann, Über die Darstellung einer Zahl als Differenz von swei Produkten. J. reine angew. Math. 164 (1931), 173–182. Zbl0001.20302
  7. G. Greaves, On the divisor-sum problem for binary cubic forms. Acta Arith. 17 (1970), 1–28. Zbl0198.37903MR263761
  8. A. E. Ingham, Some asymptotic formulae in the theory of numbers. J. London Math. Soc. 2 (1927), 202–208. Zbl53.0157.01
  9. Y. Motohashi, The binary additive divisor problem. Ann. Sci. École Norm. Sup. 27 (1994), 529–572. Zbl0819.11038MR1296556
  10. M. Robbiani, On the number of rational points of bounded height on smooth bilinear hypersurfaces in biprojective space. J. London Math. Soc. 63 (2001), 33–51. Zbl1020.11046MR1801715
  11. C. V. Spencer, The Manin Conjecture for x 0 y 0 + ⋯ + x s y s = 0 . J. Number Theory 129 (2009), 1505–1521. Zbl1171.11054MR2521490

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.