Abstract
In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a linear term in the exponent, the estimates can be further improved for almost all parameter values. Our results extend the bound for one-variable theta sums obtained by Fedotov and Klopp in 2012.
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To Peter Sarnak on the occasion of his 70th birthday
Research supported by EPSRC grant EP/S024948/1.
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Marklof, J., Welsh, M. Bounds for theta sums in higher rank. II. JAMA 151, 235–264 (2023). https://doi.org/10.1007/s11854-023-0333-9
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DOI: https://doi.org/10.1007/s11854-023-0333-9