Nonexistence of generalized bent functions and the quadratic norm form equations

Chang Lv; Yuqing Zhu

doi:10.1007/s10623-025-01606-y

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arXiv · 1804.01292

Nonexistence of generalized bent functions and the quadratic norm form equations

Chang Lv·Yuqing Zhu

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Abstract

We present a new result on the nonexistence of generalized bent functions (GBFs)from (Z/tZ)^n to Z/tZ (called type [n, t]) for a large class. Assume p is an odd prime number. By showing certain quadratic norm form equations having no integral points, we obtain a universalresult on the nonexistence of GBFs with type [n,2p^e] when p and n satisfy a certain inequality, and by computational methods with a widely accepted hypothesis, Generalized Riemann Hypothesis, we also achieve some results on the nonexistence of GBFs for relatively small p.

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Chang Lv, Yuqing Zhu. 2018-04-04. Nonexistence of generalized bent functions and the quadratic norm form equations. https://doi.org/10.1007/s10623-025-01606-y

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