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SUMMARY:Sinan Gunturk (New York University)
DTSTART:20260713T173000Z
DTEND:20260713T175500Z
DTSTAMP:20260710T111632Z
UID:CANT2026/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/16/
 ">Exponential sums and a conjecture involving quantization of bandlimited 
 functions</a>\nby Sinan Gunturk (New York University) as part of Combinato
 rial and additive number theory seminar (CANT 2026)\n\nLecture held in Sci
 ence Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nSigma-de
 lta modulation is a classical method for oversampled coarse quantization w
 hich enables approximation of bandlimited functions (e.g. audio signals) a
 t high sampling rates despite using only two fixed levels to round each sa
 mple. In the basic form of this method (the "first order" case)\, the appr
 oximation rate is $\\lambda^{-1}$ in the uniform norm where $\\lambda$ den
 otes the oversampling ratio\, but the pointwise error has been shown to de
 cay at least at the rate $\\lambda^{-4/3+\\epsilon}$ under generic conditi
 ons. Meanwhile\, a long-standing folklore conjecture based on numerical si
 mulations predicts square-root cancellation "on average"\, i.e. approximat
 ion rate of order $\\lambda^{-3/2+\\epsilon}$. We disprove the conjecture 
 for the Besicovitch norm\, utilizing certain exponential sums of bandlimit
 ed phase. Joint work with Maksym Radziwill.\n
LOCATION:https://researchseminars.org/talk/CANT2026/16/
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