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Truncations of Gauss' square exponent theorem

Ji-Cai Liu, Shan-Shan Zhao (2022)

Czechoslovak Mathematical Journal

We establish two truncations of Gauss’ square exponent theorem and a finite extension of Euler’s identity. For instance, we prove that for any positive integer n , k = 0 n ( - 1 ) k 2 n - k k ( q ; q 2 ) n - k q k + 1 2 = k = - n n ( - 1 ) k q k 2 , where n m = k = 1 m 1 - q n - k + 1 1 - q k and ( a ; q ) n = k = 0 n - 1 ( 1 - a q k ) .

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