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q-Series Related with Higher Forms

Nikolaos D. Bagis

Abstract

We examine $q-$series related to higher forms. These forms are cubics, quartics, etc. In some points, in the article we add parts from previous works, in such a way, the article be more complete and readable.

q-Series Related with Higher Forms

Abstract

We examine series related to higher forms. These forms are cubics, quartics, etc. In some points, in the article we add parts from previous works, in such a way, the article be more complete and readable.

Paper Structure

This paper contains 8 sections, 678 equations.

Table of Contents

  1. Introduction.
  2. Generalizations of Jacobi's two-square theorem
  3. Representations in cubic forms
  4. A fundamental formula for the complex integration
  5. The functional equation of $\sum^{\infty}_{n=1}\chi(n) n^{-\nu s}$
  6. Borcherds products
  7. Quadratic residues and representations in certain forms
  8. A summation formula