Analogues of the general theta transformation formula
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Publication:2837115
DOI10.1017/S0308210511001685zbMath1357.11047arXiv1111.4799MaRDI QIDQ2837115
Publication date: 10 July 2013
Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1111.4799
Related Items (18)
Some identities involving convolutions of Dirichlet characters and the Möbius function ⋮ 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 ⋮ A generalized modified Bessel function and a higher level analogue of the theta transformation formula ⋮ On a class of functions that satisfies explicit formulae involving the Möbius function ⋮ Error functions, Mordell integrals and an integral analogue of a partial theta function ⋮ Riesz-type criteria and theta transformation analogues ⋮ Certain extensions of results of Siegel, Wilton and Hardy ⋮ Some Mellin transforms for the Riemann zeta function in the critical strip ⋮ Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations ⋮ Modular-type relations associated to the Rankin-Selberg \(L\)-function ⋮ Zeros of combinations of the Riemann \(\xi\)-function on bounded vertical shifts ⋮ Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms ⋮ Superimposing theta structure on a generalized modular relation ⋮ The generalized modified Bessel function and its connection with Voigt line profile and Humbert functions ⋮ Koshliakov zeta functions I: modular relations ⋮ An exact formula for a Lambert series associated to a cusp form and the Möbius function ⋮ On special Riemann xi function formulae of Hardy involving the digamma function
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