nt.number theory – Meaning of the extended main part of weakly holomorphic modular forms

In p.312 of & # 39; Rhoades, Robert C., Linear relationships between Poincaré series through weak harmonic forms of Maass. Ramanujan J. 29 (2012), no. 1-3, 311–320 & # 39 ;, the author defines the extended main part at infinity as follows:

A weakly holomorphic modular shape is any meromorphic modular shape whose poles are supported at the cusps. The main part extended into infinity in a weakly holomorphic modular form $ f $ is the polynomial $ P_ {f, infty} in mathbb C (q ^ {- 1}) $ such that $ f (z) -P_ {f, infty} (q ^ {- 1}) = O (e ^ {- epsilon y}) $ how $ y to infty $.

My questions are

  1. What is the meaning of the extended main part?
  2. What is the relationship of this definition of extended main part and the & # 39; main part of Laurent's expansion?
  3. Is the extended main part of the weakly holomorphic modular form uniquely determined?

In addition, the author defines the main part extended at the cusps $ x $ as follows:

Yes $ x $ It is a cusp, the main part extended in $ x $ is the finite sum of terms in the Fourier expansion around $ x $ they have no rapid decline towards $ x $.

I did not understand this sentence, but in my idea the natural definition of the main part extended in $ x $ is the following:

Leave $ sigma in mathrm {SL} _2 ( mathbb R) $ be the satisfying item $ sigma x = infty $. So $ f | _k sigma ^ {- 1} $ has the Fourier expansion in $ q $, where $ q = e (z / h) $, $ h $ is the width of the cusp in $ x $. The main extended part of $ f $ to $ x $ it's a polynomial $ P_ {f, x} (q ^ {- 1}) in mathbb C (q ^ {- 1}) $ such that $ f | _k sigma ^ {- 1} (z) -P_ {f, x} (q ^ {- 1}) = O (e ^ {- epsilon y}) $.

Is my understanding correct?

web forms: add additional values ​​to "next submit value"

Every time a web form is submitted it creates a submit value, i.e. 30 and when it goes to the notification email it looks like this:

http: // localhost / sitename / admin / structure / webform / manage / contact / submit / 30

What I want it to do is have the ability to create a unique / random id for that URL, i.e.

http: // localhost / sitename / admin / structure / webform / manage / contact / submit / 30-abcd81091010

What I want to do is link the client to the submitted web form, but anyone could access any web form just by changing the number in the URL.

Anyone able to help?

forms authentication: set cookie lifetime

I have SharePoint 2016 in prem. My portal has forms based authentication. Anyone can register an account and log in to access the portal with read permission. By default, users will log out after 25 minutes. I have used the following scripts and update the lifetime of cookies.
But I want administrators to access the portal until I click the Logout button. How can you implement or increase the lifetime of cookies for a particular set of users who have Full Control permission?

$ sts = Get-SPSecurityTokenServiceConfig
$ sts.CookieLifetime = New-TimeSpan -Minutes 25
$ sts.Update ()

forms: can a header be a substitute for tags?

Chrome & # 39; s Lighthouse continues to report "Form elements have no associated tags," which web.dev provides more information on:

Labels ensure that form controls are properly advertised using assistive technologies such as screen readers. Assistive technology users rely on these labels to navigate forms. Mouse and touchscreen users also benefit from labels because the label text makes a larger click target.

However, I am not convinced that you need to make any changes to multiple forms because:

  • There is a text on the form that describes what must be completed
  • There are placeholders in the entry itself (and some also have icons)
  • The text boxes appear to be the same vertical height as the buttons (and are wider). Some of them are multi-line text areas, which are definitely a big enough target.
  • These untagged forms only have text input, or are email / password logins, so it's not difficult to keep track of where you're going

Also, I think it would be weird to wrap the above text in a tag (and unexpected), not that it works when the text refers to the two email / password fields.

Examples (square brackets indicate a text box / area with placeholders, not to scale):

Login with your email and password:


(Write your update ……

In cases like these, do I need labels?

Google Forms: How do I add "if yes, please describe" to an affirmative answer if chosen?

When using Google Forms, if the person answers yes, I want them to elaborate and give a short answer. How can I do this?

finite element method – FEM: electric field between two arbitrarily defined forms

I was wondering how to do the following:
I would like to calculate the electrostatic field between two ways using the FEM method.

(*Define Boundaries*)
air = Rectangle({-3, -3}, {3, 3});
object1 = Disk();
object2 = Rectangle({2, 0}, {2.5, 2});
Show(Graphics({Blue, air}), Graphics({Magenta, object1}),Graphics({Green, object2}))

enter the image description here

Calculation of the electric field at each point {x, y} in 2D space:

enter the image description here
$ r_i $ is the vector of the point charge; $ r $ is the vector to the point in 2D space (or also 3D) where we want to calculate the electric field.

I do a Mathematica function (for the moment I omit the constant term):

eField(x_, y_) := q Sum(({x, y} - pts((i)))/Norm({x, y} - pts((i)))^3, {i, n})

where pts((i)) are the limit points of the loaded object and x Y y are coordinates of the "air" object.

How it would proceed:

  1. I calculate the electrostatic field of object 1 -> $ E_1 $

  2. I calculate the electrostatic field of object 1 -> $ E_2 $

  3. I use superposition to get the resulting electric field: $ E_ {Total} = E_1 + E_2 $

I would really appreciate if someone could show me how to do it in Mathematica using Finite Element (FEM).

How do you customize NewForm, EditForm, and DispForm.aspx item forms in SharePoint Online?

I've been assigned a site in SharePoint Online (latest / best version), full privileges for my site collection … and zero privileges outside of that site collection.

I have SharePoint Designer 2013.

Neither InfoPath nor PowerApps are options for me.

Q: How can I customize the forms? Simple things: how to rearrange the order of some fields; hide other fields?

I looked here but I don't see any option to visually edit a form using my current versions of SharePoint Designer or SharePoint. I'm guessing both have changed since that answer was published in 2014.


Q: What tools are available to modify a "classic" SharePoint form (.aspx)? Again: InfoPath and PowerApps are not options.

Q: Are there any tutorials that can tell me to tell you enough about SharePoint aspx syntax so that I can modify forms in Notepad? Without a visual designer, SPD 2013 is little better than Notepad.

Use of Google forms and security settings

We are considering using Google Forms and we need to find out if it can be used to collect and process personal information such as Name, Address, Telephone, etc. Could someone make a recommendation based on their industry experience with Google Forms and possibly Google Map?
Is there a way to run it safely?
Thank you,

web forms: Twig if declaration doesn't work, as expected, in attached PDF

The if statements generate an error when saving the Twig template to an attached PDF complaining that the Elements (YAML) are invalid and cannot parse the line containing the if statement.

Update: Later I found that {% for%} works but {% set%} does not. Maybe there is something about Entity Print support for Twig, or Webform … hard to say.

Test works

The following statement will work in a Twig template used for the body of an email handler.

{% if data.checkbox%}
{% else%}
No coincidence
{% will end if%}

The test fails

The same code in an attached PDF generates an error.