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An explicit formula for the Fourier coefficients of Eisenstein series attached to lattices

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Abstract

We prove an explicit formula for local densities of inhomogeneous quadratic forms. The formula is derived by calculating explicitly the Fourier coefficients of various types of Eisenstein series.

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Acknowledgements

We thank the referee for suggesting many improvements to the paper. The author is supported by the Grant-in-Aid for JSPS Fellows.

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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Shunsuke Yamana

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  1. Shunsuke Yamana
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Correspondence to Shunsuke Yamana.

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The author is supported by the JSPS Institutional Program for Young Researcher Overseas Visits “Promoting international young researchers in mathematics and mathematical sciences led by OCAMI.”

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Yamana, S. An explicit formula for the Fourier coefficients of Eisenstein series attached to lattices. Ramanujan J 31, 315–352 (2013). https://doi.org/10.1007/s11139-012-9446-y

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