• Arts
• Business
• Computers
• Games
• Health
• Home
• Kids and Teens
• News
• Recreation
• Reference
• Regional
• Science
• Shopping
• Society
• Sports

EIS software

## Documentation for eis (a project by M.Kuss and J.Bruinier) ## Last modified on March 24, 2000 Contents ======== 1. What is eis? 2. How to use eis? 3. On which systems is eis running? 4. Where can I get the source code of eis? 5. Plans for improving eis in the future 6. Examples of Eisenstein series ============================================================ 1. What is eis? =============== In our paper "Eisenstein series attached to lattices and modular forms on orthogonal groups" we gave explicit formulas for computing Fourier coefficients of certain Eisenstein series attached to lattices (Theorem 4.8). To evaluate these formulas we have written eis. eis is written in C++. eis is free for non-commercial use. For comments, bugs and questions concerning eis write to one of the following addresses: [email protected] [email protected] ============================================================ 2. How to use eis? ================== Throughout this documentation we use the notation of the above paper. At the moment, eis is only running in interactive mode. Control by command line arguments is planned in the future (cf. sect. 5). To start eis just run the binary named "eis.out". At startup eis is asking you for the Gram matrix S corresponding to the lattice L. (S is an even integral matrix) You may enter S in one of the following ways: - Enter S as an array of its rows, e.g. [[6,2],[2,8]] refers to the matrix / 6 2 \ S = ( ). \ 2 8 / - Enter the letter H if S is a hyperbolic plane, e.g. H refers to the matrix / 0 1 \ S = ( ). \ 1 0 / - Enter an integer if S is a 1x1 matrix, e.g. 4 refers to the matrix S = (4). - If S is the orthogonal sum of S_1,...,S_n, then enter each of the matrices S_1,...,S_n in one of the manners above seperated by spaces. E.g. [[6,2],[2,8]] H 4 would refer to the matrix / 6 2 0 0 0 \ | | | 2 8 0 0 0 | | | S = | 0 0 0 1 0 |. | | | 0 0 1 0 0 | | | \ 0 0 0 0 4 / - To read the input (in one of the above forms) from a file, just enter the quoted

Contact Information