Báez-Duarte, L. Harmonic series summation lemma and Vasyunin’s formulas. (English. Russian original) Zbl 1093.42001 J. Math. Sci., New York 120, No. 5, 1653-1656 (2004); translation from Zap. Nauchn. Semin. POMI 282, 20-25 (2001). Summary: We introduce a mapping related to the Nyman-Beurling approach to the Riemann hypothesis. This mapping allows us to clarify the arithmetical nature of inner products for expansions of the “fractional part” functions. We also simplify the deduction of Vasyunin’s cotangent formulas. MSC: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series 11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses Keywords:cotangent formula; summation formula; arithmetic progression; harmonic series × Cite Format Result Cite Review PDF Full Text: DOI