caa a22 4500 445836199 CHVBK 20180317145331.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00209-009-0656-y doi (NATIONALLICENCE)springer-10.1007/s00209-009-0656-y Luo Wenzhi Department of Mathematics, The Ohio State University, 43210, Columbus, OH, USA aut A note on the distribution of integer points on spheres [Elektronische Daten] [Wenzhi Luo] In this note, by applying the works of Böcherer and Schulze-Pillot, we evaluate asymptotically the variance of the Linnik distribution, and show as Y → ∞, $$\label{eq1} \sum _{n \leq Y,\, n \not \equiv 0 \, (\, {\rm mod} 4)} \frac{\sum _{|x|^{2} = n} P\left( \frac{x}{|x|} \right)}{n^{1/4}} {\overline{\frac{\sum _{|z|^{2} = n} Q \left(\frac{z}{|z|} \right)}{n^{1/4}}}} = \, c < P,\, Q > \, \Lambda (1/2,\, P) \, Y + o(Y) ,$$for any spherical harmonics P, Q on S 2 which are Hecke eigenforms, where | · | is the usual Euclidean norm on R 3, and c is an explicit constant. Springer-Verlag, 2009 Equidistribution nationallicence Spherical harmonic nationallicence Quarternion algebra nationallicence Jacquet-Langlands correspondence nationallicence Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 965-970 0025-5874 267:3-4<965 2011 267 209 https://doi.org/10.1007/s00209-009-0656-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0656-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Luo Wenzhi Department of Mathematics, The Ohio State University, 43210, Columbus, OH, USA aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 965-970 0025-5874 267:3-4<965 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer