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This paper explores the properties of multipliers associated with discreteanalogues of fractional integrals, revealing intriguing connections withDirichlet characters, Euler's identity, and Dedekind zeta functions ofquadratic imaginary fields. Employing Fourier transform techniques, theHardy--Littlewood circle method, and a discrete analogue of the Stein--Weissinequality on product space through implication methods, we establish$\ell^p\rightarrow\ell^q$ bounds for these operators. Our results contribute toa deeper understanding of the intricate relationship between number theory andharmonic analysis in discrete domains, offering insights into the convergencebehavior of these operators.

On Some Multipliers Related to Discrete Fractional Integrals