تقرير
Variance of the k-fold divisor function in arithmetic progressions for individual modulus
| العنوان: | Variance of the k-fold divisor function in arithmetic progressions for individual modulus |
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| المؤلفون: | Nguyen, David T. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11B25, 11N37, 11M50 |
| الوصف: | In this paper, we confirm a smoothed version of a recent conjecture on the variance of the k-fold divisor function in arithmetic progressions to individual composite moduli, in a restricted range. In contrast to a previous result of Rodgers and Soundararajan, we do not require averaging over the moduli. Our proof adapts a technique of S. Lester who treated in the same range the variance of the k-fold divisor function in the short intervals setting, and is based on a smoothed Voronoi summation formula but twisted by multiplicative characters. The use of Dirichlet characters allows us to extend to a wider range from previous result of Kowalski and Ricotta who used additive characters. Smoothing also permits us to treat all k unconditionally. This result is closely related to moments of Dirichlet L-functions. Comment: 29 pages, added 1 figure, incorporated referee's suggestions--in particular, fixed a flaw in the original choice of the parameter N and a notational issue, exposition heavily revised |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2205.02354 |
| رقم الأكسشن: | edsarx.2205.02354 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |