Riesz-type criteria and theta transformation analogues

DOI10.1016/J.JNT.2015.08.005zbMath1396.11105OpenAlexW1764886223MaRDI QIDQ897549

Arindam Roy, Atul Dixit, Alexandru Zaharescu

Publication date: 7 December 2015

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2015.08.005

zbMATH Keywords

Riemann zeta functionMöbius functionhypergeometric functionRiemann hypothesisDirichlet \(L\)-functionRamanujanHardyFerrar

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) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (11)

Some identities involving convolutions of Dirichlet characters and the Möbius function ⋮ Riesz-type criteria for the Riemann hypothesis ⋮ Zeros of combinations of the Riemann \(\Xi\)-function and the confluent hypergeometric function on bounded vertical shifts ⋮ A modular relation involving non-trivial zeros of the Dedekind zeta function, and the generalized Riemann hypothesis ⋮ On a class of functions that satisfies explicit formulae involving the Möbius function ⋮ Hardy-Littlewood-Riesz type equivalent criteria for the generalized Riemann hypothesis ⋮ Error functions, Mordell integrals and an integral analogue of a partial theta function ⋮ Certain extensions of results of Siegel, Wilton and Hardy ⋮ Some Mellin transforms for the Riemann zeta function in the critical strip ⋮ Modular-type relations associated to the Rankin-Selberg \(L\)-function ⋮ On special Riemann xi function formulae of Hardy involving the digamma function

Cites Work

• Character analogues of Ramanujan-type integrals involving the Riemann \(\Xi \)-function
• Character analogues of theorems of Ramanujan, Koshliakov and Guinand
• Analogues of the general theta transformation formula
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