منابع مشابه
The number of representations of a number by various forms
In a recent paper, I began with four classical results due to Jacobi, Dirichlet and Lorenz which give the number of representations of a number by various forms involving squares in terms of divisor functions. I deduced another sixteen similar representation theorems involving triangular numbers and/or squares, including celebrated results of Legendre and Ramanujan (and omitted a seventeenth, g...
متن کاملJacobi Forms over Number Fields
OF THE DISSERTATION Jacobi Forms over Number Fields by Howard Skogman Doctor of Philosophy in Mathematics University of California San Diego, 1999 Professor Harold Stark, Chair We de ne Jacobi Forms over an algebraic number eld K and construct examples by rst embedding the group and the space into the symplectic group and the symplectic upper half space respectively. We then create symplectic m...
متن کاملNumber Forms in the Brain
Abstract Mental images of number lines, Galton's "number forms" (NF), are a useful way of investigating the relation between number and space. Here we report the first neuroimaging study of number-form synesthesia, investigating 10 synesthetes with NFs going from left to right compared with matched controls. Neuroimaging with functional magnetic resonance imaging revealed no difference in brain...
متن کاملTernary quadratic forms over number fields with small class number
We enumerate all positive definite ternary quadratic forms over number fields with class number at most 2. This is done by constructing all definite quaternion orders of type number at most 2 over number fields. Finally, we list all definite quaternion orders of ideal class number 1 or 2.
متن کاملCm Number Fields and Modular Forms
x∂F⊂a⊂OF (Na)k−1. Here the superscript ‘+′ stands for totally positive elements. Siegel further derived from this a simpler proof of his famous theorem that ζF (1− k) is rational for all k ≥ 1. Siegel’s construction is based on the simple observation that a Hilbert modular form becomes an elliptic modular form when restricting diagonally to the upper half plane. Indeed, Hecke constructed and pr...
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ژورنال
عنوان ژورنال: Psychological Review
سال: 1897
ISSN: 0033-295X
DOI: 10.1037/h0064635