Mixing
Calculate the limit of special sequence.
$begingroup$
There is given a sequence $A_{0},A_{1},...$ wich are all ordered zeros of Mertens fuction $M(n)$.
How to find the following limit ?:
$$lim_{ntoinfty}frac{A_{n+1}-A_{n}}{A_{n}^{0.75}}$$
Does this limit exists?
I tried to prove this by looking for some number-theoretic interpretation-wich i could not find.
How to generaly solve that kind of problems i.e. estimating the difference between two consecutive values of arithmetic functions?
I am also curious of some papers about this.
Regards
number-theory limits analytic-number-theory
asked Jan 21 at 14:49
mkultramkultra
758
$endgroup$
add a comment |
$begingroup$
There is given a sequence $A_{0},A_{1},...$ wich are all ordered zeros of Mertens fuction $M(n)$.
How to find the following limit ?:
$$lim_{ntoinfty}frac{A_{n+1}-A_{n}}{A_{n}^{0.75}}$$
Does this limit exists?
I tried to prove this by looking for some number-theoretic interpretation-wich i could not find.
How to generaly solve that kind of problems i.e. estimating the difference between two consecutive values of arithmetic functions?
I am also curious of some papers about this.
Regards
number-theory limits analytic-number-theory
asked Jan 21 at 14:49
mkultramkultra
758
$endgroup$
add a comment |
$begingroup$
There is given a sequence $A_{0},A_{1},...$ wich are all ordered zeros of Mertens fuction $M(n)$.
How to find the following limit ?:
$$lim_{ntoinfty}frac{A_{n+1}-A_{n}}{A_{n}^{0.75}}$$
Does this limit exists?
I tried to prove this by looking for some number-theoretic interpretation-wich i could not find.
How to generaly solve that kind of problems i.e. estimating the difference between two consecutive values of arithmetic functions?
I am also curious of some papers about this.
Regards
number-theory limits analytic-number-theory
asked Jan 21 at 14:49
mkultramkultra
758
$endgroup$
There is given a sequence $A_{0},A_{1},...$ wich are all ordered zeros of Mertens fuction $M(n)$.
How to find the following limit ?:
$$lim_{ntoinfty}frac{A_{n+1}-A_{n}}{A_{n}^{0.75}}$$
Does this limit exists?
I tried to prove this by looking for some number-theoretic interpretation-wich i could not find.
How to generaly solve that kind of problems i.e. estimating the difference between two consecutive values of arithmetic functions?
I am also curious of some papers about this.
Regards
number-theory limits analytic-number-theory
number-theory limits analytic-number-theory
asked Jan 21 at 14:49
mkultramkultra
758
asked Jan 21 at 14:49
mkultramkultra
758
asked Jan 21 at 14:49
mkultramkultra
758
asked Jan 21 at 14:49
mkultramkultra
758
asked Jan 21 at 14:49
mkultramkultra
758
758
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3081958%2fcalculate-the-limit-of-special-sequence%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3081958%2fcalculate-the-limit-of-special-sequence%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
