Selberg class Group - Wednesday Discussion
A webpage for each L-function
+Selberg Data \{d,q,\{eigenvalues\},\omega\} / functional equation
- +500 Dirichlet Coefficients (A link rather than direct output? Link to code/program?)
- +200 Zeros (A link rather than direct output? Link to code/program?)
- +Plot Z-function up to 20*conductor (A link rather than direct output? Link to code/program?)
+Seed: eg comes from Newform on S_4(\Gamma_0(5))
- +Special Values
- +Does it have integer coefficients?
- Is it Primitive?
- Associated to a geometric object
- Is it a lift/twist/sym^2/congruent to/etc?
- Odd facts
Items marked with a + can usually be produced by a computer program
Sources for automated generation of L-function pages
Degree 1 from Rubinstein's database of L-functions
- Degree 2 Modular forms folks
Automatically generate an L-function web page from other objects
Searching
1. MathSciNet style searching (variable fields). For example:
- Degree 2, Weight 4, Level 5
Degree 3, level 1, not a symmetric square, spectral parameter<100
2. Graphical browsing in families of L-functions: 2-dimensional grid for L-functions associated to modular forms or Maass forms.
Questions
Who will write the script to generate L-function pages from modular forms?
Interface Wishlist
- User Preferences for display (eg, don't show the graph of the Z-function, show the first few coefficients)
- Search-style page
- Search by Coefficients?
- Browser-style page