An exponentially-averaged Vasyunin formula
نویسندگان
چکیده
We prove a Vasyunin-type formula for an autocorrelation function arising from Nyman-Beurling criterion generalized to probabilistic framework. This can also be seen as reciprocity cotangent sums, related the ones proven in [BC13], [ABB17].
منابع مشابه
A Divergent Vasyunin Correction
Abstract. V. I. Vasyunin has introduced special sequences of step functions related to the strong Nyman-Beurling criterion that converge pointwise to 1 in [1,∞). We show here that the first and simplest such sequence considered by Vasyunin diverges in L1((1,∞), x dx), which of course precludes the L2((1,∞), x dx)-convergence needed for the Riemann hypothesis. Whether all sequences considered by...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2021
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/proc/15422