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20212025
most citedDouble coset operators and eta-quotients

4 citations · 4 across the 11 of their papers we have counts for

collaborators

11 papers

math.NT2025

Quadratic Gauss sums over : explicit formulas, a duality theorem, and applications to Weil representations and cubic hypersurfaces over

Xiao-Jie Zhu

We provide explicit formulas for quadratic Gauss sums over , which generalize some of the existing formulas, e.g., Skoruppa and Zagier's (for ), an…

math.NT2025

Correspondence among congruence families for generalized Frobenius partitions via modular permutations

Rong Chen, Xiao-Jie Zhu

In 2024, Garvan, Sellers and Smoot discovered a remarkable symmetry in the families of congruences for generalized Frobenius partitions and . They also emphasi…

math.NT2024

A formula for Fourier coefficients of certain eta-quotients and their expansions as Eisenstein series

Xiao-Jie Zhu

We give a list of holomorphic eta-quotients of integral weight ( of which are primitive) and provide a uniform closed formula for their Fourier coefficients where…

math.NT2024

Dimension formulas for modular form spaces of rational weights, the classification of eta-quotient characters and an extension of Martin's theorem

Xiao-Jie Zhu

We give an explicit formula for dimensions of spaces of rational-weight modular forms whose multiplier systems are induced by eta-quotients of fractional exponents. As the first ap…

math.NT2024

Transformation properties of Andrews-Beck functions and generalized Appell-Lerch series

Rong Chen, Xiao-Jie Zhu

In 2021, Andrews mentioned that George Beck introduced a partition statistic which is related to Dyson's rank statistic. Motivated by Andrews's work, scholars have esta…

math.NT2024

Explicit formulae for linear characters of

Xiao-Jie Zhu

We give explicit formulae for a class of complex linear unitary characters of the congruence subgroups which involve a variant of Rademacher's function. We then prove…