BASES FOR Sk(Γ1(4)) AND FORMULAS FOR EVEN POWERS OF THE JACOBI THETA FUNCTION

DOI10.1142/S1793042113500693zbMath1282.11033MaRDI QIDQ2870226

Yifan Yang, Shinji Fukuhara

Publication date: 17 January 2014

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

sum of squaresFourier coefficients of modular formsperiod polynomialsmodular forms (one variable)

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11)

Cites Work

• A basis for \(S_k(\Gamma_0(4))\) and representations of integers as sums of squares
• Eine Verallgemeinerung der Abelschen Integrale
• On integrals attached to automorphic forms
• Representations of integers as sums of 32 squares
• Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions
• Representations of integers as sums of an even number of squares
• RECENT PROGRESS IN THE STUDY OF REPRESENTATIONS OF INTEGERS AS SUMS OF SQUARES
• Period polynomials and explicit formulas for Hecke operators on Γ₀(2)
• A SHORT PROOF OF MILNE'S FORMULAS FOR SUMS OF INTEGER SQUARES

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