# Jonathan Hanke's Website

Research and Software in Number Theory

## Some Tikz References

J.S. Milne’s Tikz/PGF Quick Reference: pdf

Wikibooks Tikz Reference: html

TeXample Tikz Information: html

TikZit: Graphical Tikz/PGF Editor: html

Written by jonhanke

October 29th, 2012 at 6:17 am

## Algebraic/Arithmetic Geometry Online

• The Stacks Project — A large reference project for Algebraic Geometry online, meant to give the necessary background for understanding algebraic stacks.

Written by jonhanke

May 1st, 2012 at 7:50 pm

## Trace Formula References

### Basic Trace Formula References:

• LNM 1001 — The Selberg Trace Formula for PSL(2,R)
• LNM 1040 — Local Analysis of Selberg’s Trace Formula
• Knightly and Li — “Traces of Hecke operators” book
• Zagier’s Appendix in Lang’s “Introduction to Modular Forms” book
• Miyake’s Book “Modular Forms” — Chapter on the Trace formula
• Lang’s book “$\mathrm{SL}_2(\mathBbb{R})$” — Discusses the spectral theory of $\mathrm{SL}_2(\mathBbb{R})$
• Chapter 10 of Iwaniec’s book “Introduction to the Spectral Theory of Automorphic Forms”

Written by jonhanke

April 29th, 2012 at 5:45 pm

## Useful Databases

Written by jonhanke

April 29th, 2012 at 5:39 pm

## ECLIB with quadratic character (with John Cremona; C++)

Description: A modified version of John Cremona’s ECLIB libraries to compute weight 2 modular symbols for $\Gamma_0(N)$, now allowing a quadratic character.

Status: in progress

Released: April 2011

Size: Modified ???? lines of code.