Managing Editor: Bruinier, Jan Hendrik
Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna
IMPACT FACTOR 2018: 0.867
CiteScore 2018: 0.71
SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964
Mathematical Citation Quotient (MCQ) 2018: 0.71
On the fourth derivative test for exponential sums
We give an upper bound for the exponential sum ∑m=1,...,M exp(2iπf(m)) where f is a real-valued function whose fourth derivative has the order of magnitude λ > 0 small. Van der Corput's classical bound, in terms of M and λ only, involves the exponent 1/14. We show how this exponent may be replaced by any θ < 1/12 without further hypotheses. The proof uses a recent result by Wooley on the cubic Vinogradov system.
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