An error term of Ramanujan

Error estimates of Ramanujan-type series

✍ Cristinel Mortici 📂 Article 📅 2011 🏛 Springer US 🌐 English ⚖ 362 KB

On an Error Term of Chowla, I

✍ Jianya Liu 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 284 KB

Let E(x; r) be the error term in the mean-value estimate of (.(n)Ân) r , where .(n) is the Euler totient function, and r is a positive real number. We show that where c is a positive constant, and =(x ; r) is a certain function tending to 0 as x Ä . These results generalize those of Pillai and Chow

On an Error Term of Chowla, II

✍ Jianya Liu 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 277 KB

Let E(x; r) be the error term in the mean-value estimate of (.(n)Ân) r , where .(n) is the Euler totient function, and r is a positive real number. We prove in this paper that where c is a positive constant depending on r. This generalizes the earlier results of Chowla and of Bellman.

On an Error Term of Chowla, III

✍ Jianya Liu 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 240 KB

Let E(x; r) be the error term in the mean-value estimate of (.(n)Ân) r , where .(n) is the Euler totient function, and r is a positive integer. We prove in this paper that This generalizes the earlier result of Montgomery.

Note on an integral of Ramanujan

✍ J.-P. Allouche 📂 Article 📅 2006 🏛 Springer US 🌐 English ⚖ 158 KB

On an asymptotic series of Ramanujan

✍ Yaming Yu 📂 Article 📅 2009 🏛 Springer US 🌐 English ⚖ 282 KB