Representations by sextenary quadratic forms with coefficients 1,2,3 and 6 and on newforms in S₃ (Γ₀ (24), χ)

2017/05/03 by Zafer Selçuk Aygin, Zafer Selcuk Aygin, Aygin, Zafer Selcuk
Mathematics · #11E20 #11E25 #11F11 #11F20 #11F27 #11F30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11E20 #msc:11E25 #msc:11F11 #msc:11F20 #msc:11F27 #msc:11F30

paper · pdf · doi:10.48550/arxiv.1705.01244

arxiv created 2017/05/03 · openalex publication_date 2017/05/03 · arxiv updated 2017/05/04 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We use theory of modular forms to give formulas for N(1^l₁,2^l₂,3^l₃,6^l₆;n) for all l₁,l₂,l₃,l₆ ∈ ℕ₀, with l₁+l₂+l₃+l₆=6. We also apply our results to write newforms in S₃ (Γ₀ (24), χ) in terms of eta quotients.

Related

• Representations by sexternary quadratic forms with coefficients 1,2,5 and 10
• On the number of representations by certain octonary quadratic forms with coefficients 1, 2, 3, 4 and 6
• On the number of representations of certain quadratic forms and a formula for the Ramanujan Tau function
• Representations by octonary quadratic forms with coefficients 1, 2, 3 or 6
• On the representations of a positive integer by certain classes of quadratic forms in eight variables