Binary quadratic forms and the Fourier coefficients of certain weight 1 eta -quotients
نویسندگان
چکیده
منابع مشابه
Mixed Sums of Triangular Numbers and Certain Binary Quadratic Forms
In this paper, we prove that for d = 3, . . . , 8, every natural number can be written as tx+ty +3tz +dtw, where x, y, z, and w are nonnegative integers and tk = k(k+1)/2 (k = 0, 1, 2, . . .) is a triangular number. Furthermore, we study mixed sums of triangular numbers and certain binary quadratic forms.
متن کاملRepresentations of integers by certain positive definite binary quadratic forms
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n= x2 +Ny2 for a squarefree integer N .
متن کاملFourier Coefficients of Half - Integral Weight Modular Forms modulo `
S. Chowla conjectured that every prime p has the property that there are infinitely many imaginary quadratic fields whose class number is not a multiple of p. Gauss’ genus theory guarantees the existence of infinitely many such fields when p = 2, and the work of Davenport and Heilbronn [D-H] suffices for the prime p = 3. In addition, the DavenportHeilbronn result demonstrates that a positive pr...
متن کاملFourier Coefficients of Modular Forms
These notes describe some conjectures and results related to the distribution of Fourier coefficients of modular forms. This is a rough draft and these notes should forever be considered incomplete.
متن کاملOn Spaces of Modular Forms Spanned by Eta-quotients
An eta-quotient of levelN is a modular form of the shape f(z) = ∏ δ|N η(δz) rδ . We study the problem of determining levels N for which the graded ring of holomorphic modular forms for Γ0(N) is generated by (holomorphic, respectively weakly holomorphic) eta-quotients of level N . In addition, we prove that if f(z) is a holomorphic modular form that is nonvanishing on the upper half plane and ha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2014
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2013.08.016