Representations of Positive Integers by Positive Quadratic Forms


Tekcan A., Özkoç Öztürk A., Gezer B., Bizim O.

SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, vol.35, no.1, pp.137-148, 2011 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 1
  • Publication Date: 2011
  • Journal Name: SOUTHEAST ASIAN BULLETIN OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.137-148
  • Keywords: Representations of positive integers by positive definite quadratic forms, Generalized theta series, Eisenstein series, Cusp form
  • Bursa Uludag University Affiliated: Yes

Abstract

In this work we consider the representations of positive integers by quadratic forms F-1 = x(1)(2) + x(1)x(2) + 8x(2)(2) and G(1) = 2x(1)(2) + x(1)x(2) + 4x(2)(2) of discriminant 31 and we obtain some results concerning the modular forms (sci) (T; F, phi(tau s)). Moreover we construct a basis for the cusp form space S-4 (Gamma(0) (31), 1), and then we give some formulas for the number of representations of positive integer n by positive definite quadratic forms.