A $q$-analog of Jacobi's two squares formula and its applications
| Autor: | Rodriguez Caballero, José Manuel |
|---|---|
| Přispěvatelé: | Kotyada, Srinivas |
| Rok vydání: | 2018 |
| Předmět: |
Mathematics::Combinatorics
Mathematics - Number Theory q-analog Mathematics::Number Theory [MATH] Mathematics [math] Computer Science::Computational Geometry 11C08 11E25 11N13 Jacobi's two squares formula primitive Pythagorean triplet Computer Science::Discrete Mathematics FOS: Mathematics Number Theory (math.NT) [MATH]Mathematics [math] Computer Science::Data Structures and Algorithms |
| DOI: | 10.48550/arxiv.1801.03134 |
| Popis: | We consider a $q$-analog $r_2(n, q)$ of the number of representations of an integer as a sum of two squares $r_2(n)$. This $q$-analog is generated by the expansion of a product that was studied by Kronecker and Jordan. We generalize Jacobi's two squares formula from $r_2(n)$ to $r_2(n, q)$. We characterize the signs in the coefficients of $r_2(n, q)$ using the prime factors of $n$. We use $r_2(n, q)$ to characterize the integers which are the length of the hypotenuse of a primitive Pythagorean triangle. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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