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

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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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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Keywords

  • Eisenstein series
  • Local density
  • Jacobi forms

Mathematics Subject Classification

  • 11F30
  • 11F27