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| 2022-12-18 21:48:05 +0200 | received badge | ● Popular Question (source) |
| 2022-12-05 11:54:58 +0200 | commented answer | How to write a p-adic exponent b^k as a Power series in k ? Thank you. |
| 2022-12-05 11:54:42 +0200 | marked best answer | How to write a p-adic exponent b^k as a Power series in k ? Let $b$ be p-adic number, we write $b$ as a Power series in $p$ with a given precison. Is It possible to write $b^k$ as a Power series in $k$, with $k$ an integer ? An example : Let $\gamma_1$ and $\gamma_2$ be the 3-adic unit roots of the quadratic equations $x^2+x+3=0$ and $x^2+2x+3=0$ respectively. Let $k$ be an integer. Let $$c(k) = \frac{\gamma_1^k}{\gamma_1^2 -3} + \frac{\gamma_2^k}{\gamma_2^2 -3} + 1$$ The problem is to show that $$v_3(c(k) - 9(-1+4k^2)-27(k^3 + k^4))\geq 4.\qquad (1)$$ I know how to write $\gamma_1$ and $\gamma_2$ as a 3-adic power series with given precision, but have no idea how to work with the exponent. I've tried (1) for k integer between 1 and 100 and the inequality is true only for even numbers. For odd numbers, the left side of (1) is zero. The inequality (1) is from the article Numerical experiments on families of modular forms by Coleman, Stevens, and Teitelbaum, page 7. |
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| 2022-12-04 20:04:51 +0200 | edited question | How to write a p-adic exponent b^k as a Power series in k ? How to write a p-adic exponent b^k as a Power series in k ? Let $b$ be p-adic number, we write $b$ as a Power series in |
| 2022-12-04 11:33:07 +0200 | edited question | How to write a p-adic exponent b^k as a Power series in k ? How to write a p-adic exponent b^k as a Power series in k ? Let $b$ be p-adic number, we write $b$ as a Power series in |
| 2022-12-04 11:29:24 +0200 | edited question | How to write a p-adic exponent b^k as a Power series in k ? How to write a p-adic exponent b^k as a Power series in k ? Let $b$ be p-adic number, we write $b$ as a Power series in |
| 2022-12-03 15:43:49 +0200 | received badge | ● Student (source) |
| 2022-12-01 22:50:20 +0200 | edited question | How to write a p-adic exponent b^k as a Power series in k ? How to write a p-adic exponent b^k as a Power series in k ? Let b be p-adic number, we write b as a Power series in p wi |
| 2022-12-01 22:48:41 +0200 | commented question | How to write a p-adic exponent b^k as a Power series in k ? Let assume that k is an integer. |
| 2022-12-01 18:00:27 +0200 | edited question | How to write a p-adic exponent b^k as a Power series in k ? How to write a p-adic exponent b^k as a Power series in k ? Let b and k be p-adic numbers, we write b as a Power series |
| 2022-12-01 17:56:55 +0200 | commented question | How to write a p-adic exponent b^k as a Power series in k ? No, It is a p-adic number. The formula is an application of Koike`s trace formula. |
| 2022-12-01 13:45:52 +0200 | received badge | ● Editor (source) |
| 2022-12-01 13:45:52 +0200 | edited question | How to write a p-adic exponent b^k as a Power series in k ? How to write a p-adic exponent b^k as a Power series in k ? Let b and k be p-adic numbers, we write b as a Power series |
| 2022-11-26 13:51:22 +0200 | asked a question | How to write a p-adic exponent b^k as a Power series in k ? How to write a p-adic exponent b^k as a Power series in k ? Let b and k be p-adic numbers, we write b as a Power series |
| 2022-07-13 18:16:51 +0200 | asked a question | Koike's Trace Formula Koike's Trace Formula Koike's Trace Formula states that \begin{equation} \mbox{Tr}((U_p^{\kappa})^n) = - \sum_{0 \leq u |
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.