Fix n. Let r(n) denote the largest number r for which there is all r x n (1.- 1)- matrix H satisfying the matrix equation HHtau = nI(r). The Hadamard conjecture sates that for n divisible by 4 we have r(n) = n. Let epsilon > 0. In this paper, we show that the Extended Riemann hypothesis;rnd Ic cont results on the asymptotic existence of Hadamard matrices imply that for n sufficiently large r(n) > (1/2 - epsilon) n. (C) 2001 Academic Press. [References: 6]
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机译：修复n。令r（n）表示最大数目r，对于该数目最大的所有r x n（1-1）-矩阵H都满足矩阵方程HHtau = nI（r）。 Hadamard猜想认为，对于可被4整除的n，我们有r（n）= n。令epsilon>0。在本文中，我们证明了扩展Riemann假设; rnd Ic cont表示Hadamard矩阵的渐近存在，意味着对于n足够大的r（n）>（1/2-epsilon）n。 （C）2001学术出版社。 [参考：6]
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