Sums of squares in ℤ [ k ]

Fernando Chamizo

Journal de théorie des nombres de Bordeaux (1997)

  • Volume: 9, Issue: 1, page 25-39
  • ISSN: 1246-7405

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Chamizo, Fernando. "Sums of squares in $\mathbb {Z}[\sqrt{k}]$." Journal de théorie des nombres de Bordeaux 9.1 (1997): 25-39. <http://eudml.org/doc/248012>.

@article{Chamizo1997,
abstract = {},
author = {Chamizo, Fernando},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {circle problem; real quadratic rings; spectral theory; asymptotic formula; estimation of automorphic -functions},
language = {eng},
number = {1},
pages = {25-39},
publisher = {Université Bordeaux I},
title = {Sums of squares in $\mathbb \{Z\}[\sqrt\{k\}]$},
url = {http://eudml.org/doc/248012},
volume = {9},
year = {1997},
}

TY - JOUR
AU - Chamizo, Fernando
TI - Sums of squares in $\mathbb {Z}[\sqrt{k}]$
JO - Journal de théorie des nombres de Bordeaux
PY - 1997
PB - Université Bordeaux I
VL - 9
IS - 1
SP - 25
EP - 39
AB -
LA - eng
KW - circle problem; real quadratic rings; spectral theory; asymptotic formula; estimation of automorphic -functions
UR - http://eudml.org/doc/248012
ER -

References

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  3. [Fr] F. Fricker, Einführung in die Gitterpunktlehre, vol. 73, Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften; Math. Reihe, Birkhaüser Verlag, 1982. Zbl0489.10001MR673938
  4. [Ga] C.F. Gauss, De nexu inter multitudinem classium in quas formae binariae secundi gradus distribuntur, eaurumque determinatem [II], Werke V.2, (1839), 269-291. 
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  6. [Gr-Ry] I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series and Products, Fifth edition, (Editor: A. Jeffrey), Academic Press, 1994. Zbl0918.65002MR1243179
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  11. [Iw2] H. Iwaniec, Introduction to the Spectral Theory of Automorphic Forms, Biblioteca de la Revista Matemática Iberoamericana, Madrid, 1995. Zbl0847.11028MR1325466
  12. [Iw-Sa] H. Iwaniec and P. Sarnak, L∞ norms of eigenfunctions of arithmetic surfaces, Ann. of Math.141 (1995), 301-320. Zbl0833.11019
  13. [Kl] H.D. Kloosterman, On the representation of numbers in the form ax2 + by2 + cz2 + dt2, Acta Mathematica49 (1926), 407-464. JFM53.0155.01
  14. [La] E. Landau, Über Gitterpunkte in mehrdimensionalen Ellipsoiden, Math. Zeitschrift21 (1924), 126-132. Zbl50.0118.01MR1544690JFM50.0118.01
  15. [Lu] W. Luo, The spectral mean value for linear forms in twisted coefficients of cusp forms, Acta Arithmetica70 (1995), 377-391. Zbl0821.11035MR1330741
  16. [Ph-Ru] R.S. Phillips and Z. Rudnick, The circle problem in the hyperbolic plane, J. Funct. Anal.121 (1994), 78-116. Zbl0812.11035MR1270589
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