级数范数的统一界及其算术应用

IF 0.8 3区数学 Q3 MATHEMATICS

Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2020-12-08 DOI:10.1017/S0305004122000081

F. Waibel

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引用次数: 2

摘要

摘要证明了theta级数的倒角部分的Petersson范数的一致界。给出了二次型表示次数的改进渐近公式。作为一个应用，我们证明了每一个整数$n \neq 0,4,7 \，(\textrm{mod}\ 8)$表示为$n= x_1^2 + x_2^2 + x_3^3$对于整数$x_1,x_2,x_3$，使得乘积$x_1x_2x_3$最多有72个质因数。

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Uniform bounds for norms of theta series and arithmetic applications

Abstract We prove uniform bounds for the Petersson norm of the cuspidal part of the theta series. This gives an improved asymptotic formula for the number of representations by a quadratic form. As an application, we show that every integer $n \neq 0,4,7 \,(\textrm{mod}\ 8)$ is represented as $n= x_1^2 + x_2^2 + x_3^3$ for integers $x_1,x_2,x_3$ such that the product $x_1x_2x_3$ has at most 72 prime divisors.

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来源期刊

Mathematical Proceedings of the Cambridge Philosophical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.