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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…
Primitively universal quaternary quadratic forms
Jangwon Ju, Daejun Kim, Kyoungmin Kim +2
A (positive definite and integral) quadratic form is said to be if it represents all positive integers, and is said to be …
The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma
Jangwon Ju, Daejun Kim
In this article, we study the representability of integers as sums of pentagonal numbers, where a pentagonal number is an integer of the form for some non…
Prime-universal diagonal quadratic forms
Jangwon Ju, Daejun Kim, Kyoungmin Kim +2
A (positive definite and integral) quadratic form is said to be if it represents all primes. Recently, Doyle and Williams in [2] classified all prime-uni…
Representations of finite number of quadratic forms with same rank
Daejun Kim, Byeong-Kweon Oh
Let be positive integers with . Let be the largest integer such that for any (positive definite and integral) quadratic forms of rank $…
A sum of three nonunit squares of integers
Daejun Kim, Jeongwon Lee, Byeong-Kweon Oh
We say a positive integer is a sum of three nonunit squares if it is a sum of three squares of integers other than one. In this article, we find all integers which are sums of thre…