## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, December 05, 2013, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Chandan Dubey

## Counting solutions of Quadratic equations over quotient rings

An $n$-ary integral quadratic form is a quadratic equation over integers in $n$ variables (denoted by $Q(x_1,\cdots,x_n)$). Integral quadratic forms appear in many areas of computer science e.g., lattices, cryptography, embeddings. We study integral quadratic forms over the ring $Z/p^kZ$, where $p$ is an odd prime. In particular, given and integral quadratic form $Q(x_1,\cdots,x_n)$ and a $t \in Z$, we want to count the number of solutions of $Q(x_1,\cdots,x_n)=t \pmod{p^k}$. This talk will be introductory. It will be aimed at providing a better understanding of quadratic forms and a brief connection to lattices and cryptography.

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