, Volume 52, Issue 3, pp 3056-3063

Arithmetic of quaternions and Eisenstein series

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Abstract

In the paper one computes the Fourier coefficients of the Eisenstein series of the orthogonal group of signature (1, 4). The formulas show that the restriction of the Eisenstein series to the “imaginary” axis is a Dirichlet series, whose coefficients are the products of the L-series by the number of the representations of the given number as a sum of three squares.

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 160, pp. 82–90, 1987.