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On the representation numbers satisfying partially multiplicative relations
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-02-22 , DOI: 10.1016/j.jnt.2021.01.006
Ick Sun Eum

Let rQ(n) be the representation number of a nonnegative integer n by an integral positive definite quadratic form Q in 2k variables. Let N be the level of Q. For a fixed prime pN, we assume that rQ(n) satisfies the relation rQ(1)rQ(p2n)=rQ(p2)rQ(n) for all positive integers n with pn. We actually show that this relation holds for any prime pN when (1)kN is a fundamental discriminant.



中文翻译:

关于满足部分乘法关系的表示数

[Rñ是2 k个变量中整数正定二次型Q的非负整数n的表示数。令NQ的水平。对于固定的素数pñ,我们假设 [Rñ 满足关系 [R1个[Rp2ñ=[Rp2[Rñ对于所有正整数ñpñ。我们实际上表明,这种关系适用于任何素数pñ 什么时候 -1个ķñ 是根本的区别。

更新日期:2021-02-24
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