Behavior of the Dedekind's function over first order theta function according to conditions modular form. From: Journal of Mathematics and Statistics | Date: July 1, 2006| Author: | COPYRIGHT 2006 Science Publications. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan.  All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information) Copyright information

Abstract: The effect Dedekind's etha function on theta functions is analyzed according to the characteristics of theta functions under modular group conditions.

Key words: Theta functions, characteristic values, modular group, dedekind functions

INTRODUCTION

By [SL.sub.2] we mean the group of 2x2 matrices with determinant 1. We write [SL.sub.2](R) for those elements of [SL.sub.2] having coefficients in a ring R. In practice, the ring R will be integers Z, rational numbers Q and real numbers R. We call [SL.sub.2](Z) the modular group [GAMMA].

If L is lattice in ...

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