JournalsprimsVol. 41 , No. 3DOI 10.2977/prims/1145475226

Positivity of Eta Products—a Certain Case of K. Saito’s Conjecture

  • Tomoyoshi Ibukiyama

    Osaka University Graduate School of Science, Japan
Positivity of Eta Products—a Certain Case of K. Saito’s Conjecture cover

Abstract

We prove that for any prime p, the Fourier coeffcients of η(_p_τ)p/η(τ) are all non-negative, where η(τ) is the Dedekind eta function. This is a proof of some parts of K. Saito’s conjecture on such positivity of eta products associated with regular systems of weight.