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On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms

Anne-Maria Ernvall-Hytönen, Kimmo Karppinen, On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms . International Mathematics Research Notices 2008, 2008.

Abstract:

We improve known estimates for the linear exponential sums containing
Fourier coefficients of holomorphic cusp forms and show that in some
cases, our bound is actually sharp. We also briefly visit nonlinear exponential sums, and prove some results concerning the density of
rational numbers satisfying certain conditions.

BibTeX entry:

@ARTICLE{jErKa08a,
  title = {On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms  },
  author = {Ernvall-Hytönen, Anne-Maria and Karppinen, Kimmo},
  journal = {International Mathematics Research Notices},
  volume = {2008},
  year = {2008},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

Publication Forum rating of this publication: level 3

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