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math.NT2022
Theta series of ternary quadratic lattice cosets
Ben Kane, Daejun Kim
In this paper, we consider the decomposition of theta series for lattice cosets of ternary lattices. We show that the natural decomposition into an Eisenstein series, a unary theta…
math.NT2022★ 1 cited
Explicit Class number formulas for Siegel--Weil averages of ternary quadratic forms
Ben Kane, Daejun Kim, Srimathi Varadharajan
In this paper, we investigate the interplay between positive-definite integral ternary quadratic forms and class numbers. We generalize a result of Jones relating the theta functio…
math.NT2022
Universal sums of generalized heptagonal numbers
Ramanujam Kamaraj, Ben Kane, Ryoko Tomiyasu
In this paper, we consider representations of integers as sums of generalized heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum.…