On some symmetries of the base $ n $ expansion of $ 1/m $ : The Class Number connection
| Autor: | Chakraborty, Kalyan, Krishnamoorthy, Krishnarjun |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Pacific J. Math. 319 (2022) 39-53 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/pjm.2022.319.39 |
| Popis: | Suppose that $ m\equiv 1\mod 4 $ is a prime and that $ n\equiv 3\mod 4 $ is a primitive root modulo $ m $. In this paper we obtain a relation between the class number of the imaginary quadratic field $ \Q(\sqrt{-nm}) $ and the digits of the base $ n $ expansion of $ 1/m $. Secondly, if $ m\equiv 3\mod 4 $, we study some convoluted sums involving the base $ n $ digits of $ 1/m $ and arrive at certain congruence relations involving the class number of $ \Q(\sqrt{-m}) $ modulo certain primes $ p $ which properly divide $ n+1 $. Comment: Final version |
| Databáze: | arXiv |
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