Arithmetic of quaternions and Eisenstein series
- V. A. Gritsenko
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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.
- B. A. Venkov, Selected Works. Studies in Number Theory [in Russian], Nauka, Leningrad (1981).
- A. B. Venkov, “The spectral theory of automorphic functions”, Trudy Mat. Inst. Akad. Nauk SSSR,153, 1–171 (1981).
- V. A. Gritsenko, “The zeta function of degree six for Hermitian modular forms of genus 2”, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,154, 46–66 (1986).
- Yu. V. Linnik, “Quaternions and Cayley numbers; some applications of the arithmetic of quaternions”, Usp. Mat. Nauk,4, No. 5, 49–98 (1949).
- G. Shimura, “On the holomorphy of certain Dirichlet series”, Proc. London Math. Soc. Ser. 3,31, No. 1, 79–98 (1975).
- Arithmetic of quaternions and Eisenstein series
Journal of Soviet Mathematics
Volume 52, Issue 3 , pp 3056-3063
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