Zeros of combinations of the Riemann \(\xi\)-function on bounded vertical shifts

DOI10.1016/j.jnt.2014.10.004zbMath1381.11065OpenAlexW2049396390MaRDI QIDQ2254229

Alexandru Zaharescu, Arindam Roy, Atul Dixit, Nicolas Robles

Publication date: 4 February 2015

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2014.10.004

zbMATH Keywords

zerosRiemann zeta-functioncritical lineRamanujan's lost notebookself-reciprocal functionsbounded vertical shiftstheta transformation formula

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (8)

Zeros of combinations of the Riemann \(\Xi\)-function and the confluent hypergeometric function on bounded vertical shifts ⋮ A generalized modified Bessel function and a higher level analogue of the theta transformation formula ⋮ Koshliakov kernel and identities involving the Riemann zeta function ⋮ Polynomial moments with a weighted zeta square measure on the critical line ⋮ Certain extensions of results of Siegel, Wilton and Hardy ⋮ Some Mellin transforms for the Riemann zeta function in the critical strip ⋮ The \(a\)-values of the Riemann zeta function near the critical line ⋮ On special Riemann xi function formulae of Hardy involving the digamma function

Cites Work

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• Arithmetic progressions of zeros of the Riemann zeta function
• Analogues of the general theta transformation formula
• Diskrete Mittel für einige Zetafunktionen.
• SOME SELF-RECIPROCAL FUNCTIONS
• The Riemann Zeta Function on Arithmetic Progressions
• Some Solutions of the Equation F (t ) = F (t ⁻¹ )
• Some Formulae for the Riemann Zeta-Function
• On the Non-Periodicity of the Zeros of the Riemann Zeta-Function
• Remarks on Periodic Sequences and the Riemann Zeta-Function
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