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We consider four classes of polynomials over the fields , , , , , , , where . We find sufficient conditions on the pairs for which these polynomials permute and we give lower bounds on the number of such pairs. 相似文献
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《Discrete Mathematics》2022,345(9):112970
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《Journal of Functional Analysis》2023,284(7):109835
We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator in dimension , where , and is and compactly supported. The weighted resolvent norm grows no faster than , while an exterior weighted norm grows . We introduce a new method based on the Mellin transform to handle the two-dimensional case. 相似文献
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Let χ be an order c multiplicative character of a finite field and a binomial with . We study the twisted classical and T-adic Newton polygons of f. When , we give a lower bound of Newton polygons and show that they coincide if p does not divide a certain integral constant depending on .We conjecture that this condition holds if p is large enough with respect to by combining all known results and the conjecture given by Zhang-Niu. As an example, we show that it holds for . 相似文献
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Let M be a random rank-r matrix over the binary field , and let be its Hamming weight, that is, the number of nonzero entries of M.We prove that, as with r fixed and tending to a constant, we have that converges in distribution to a standard normal random variable. 相似文献
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