Nonexistence of generalized bent functions and the quadratic norm form equations

04/04/2018

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by   Chang Lv, et al.

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We obtain the nonexistence of generalized bent functions (GBFs) from (/t)^n to /t (called type [n,t]), for a large new class. Specifically, by showing certain quadratic norm form equations have no integral points, we obtain the universal nonexistence of GBFs with type [n, 2p^e] for all sufficiently large p with respect to n and (p-1)/_2(p), and by computational methods with a well accepted hypothesis (generalized Riemann hypothesis), we also guarantee some nonexistence results for relative small prime p.