2023/05/11 by Jens Marklof, Marklof, Jens, Matthew Welsh +1
Mathematics · #11F27 (Primary) 11L15 #37A17 (Secondary) #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2305.06995
openalex publication_date 2023/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.