Sums of squares and products of Bessel functions

DOI10.1016/j.aim.2018.09.001zbMath1451.11024arXiv1701.07460OpenAlexW2584590222WikidataQ129272584 ScholiaQ129272584MaRDI QIDQ1789491

Yanyan Li

Publication date: 10 October 2018

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.07460

zbMATH Keywords

sums of squaresBessel functionsanalytic continuationVoronoï summation formula

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Analytic continuation of functions of one complex variable (30B40)

Related Items (7)

Explicit transformations of certain Lambert series ⋮ Two general series identities involving modified Bessel functions and a class of arithmetical functions ⋮ Certain extensions of results of Siegel, Wilton and Hardy ⋮ Identities associated to a generalized divisor function and modified Bessel function ⋮ Analogue of a Fock-type integral arising from electromagnetism and its applications in number theory ⋮ SUMS OF SQUARES AND PARTITION CONGRUENCES ⋮ A class of identities associated with Dirichlet series satisfying Hecke’s functional equation

Uses Software

• DLMF

Cites Work

• Concordance and the harmonic analysis of sequences
• Hecke's functional equation and arithmetical identities
• Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann
• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• On Dirichlet series for sums of squares
• On Poisson's summation formula
• Koshliakovs Formula and Guinands Formula in Ramanujans Lost Notebook
• INTEGRALS FOR THE PRODUCT OF TWO BESSEL FUNCTIONS (II)
• SOME SUMMATIONS OVER THE LATTICE POINTS OF A CIRCLE (I)
• On a theorem of A. I. Popov on sums of squares
• Sums of Squares and Cusp Forms
• Explicit bounds for the number of 𝑝-core partitions
• Identities Involving the Coefficients of a Class of Dirichlet Series. III
• Identities Involving the Coefficients of a Class of Dirichlet Series. V
• COMPLEX FOURIER--BESSEL TRANSFORMS
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