منابع مشابه
Singular Values of Some Modular Functions *
. We denote by A1(N) and A0(N) the modular function fields with respect to Γ1(N) and Γ0(N) respectively. Let E be a set of triples of integers a = [a1, a2, a3] with the properties 0 < ai ≤ N/2 and ai 6= aj for i 6= j. For an element τ of complex upper half plane H, we denote by Lτ the lattice in C generated by 1 and τ . Let ℘(z;Lτ ) be the Weierstrass ℘-function relative to the lattice Lτ . For...
متن کاملSingular values of convex functions of matrices
Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$ are nonzero matrices and each $X_{i}$ is positive semidefinite. It is shown that if $f$ is a nonnegative increasing convex function on $left[ 0,infty right) $ satisfying $fleft( 0right) =0 $, then $$2s_{j}left( fleft( fra...
متن کاملOn the singular values of Weber modular functions
The minimal polynomials of the singular values of the classical Weber modular functions give far simpler defining polynomials for the class fields of imaginary quadratic fields than the minimal polynomials of singular moduli of level 1. We describe computations of these polynomials and give conjectural formulas describing the prime decomposition of their resultants and discriminants, extending ...
متن کاملTraces of Cm Values of Modular Functions
Zagier proved that the traces of singular moduli, i.e., the sums of the values of the classical j-invariant over quadratic irrationalities, are the Fourier coefficients of a modular form of weight 3/2 with poles at the cusps. Using the theta correspondence, we generalize this result to traces of CM values of (weakly holomorphic) modular functions on modular curves of arbitrary genus. We also st...
متن کاملAlgebraicity of Singular Values and Arithmetic of Principal Modular Forms
In this thesis, we prove several results on the algebraicity of values of certain modular functions. More precisely, let f(z) be a modular form for the congruence group Γ0(N). We show that f(τ) is an element in the ring class field for the order Oτ corresponding to τ whenever τ is the fixed point of a specific class of matrices in the normalizer of Γ0(N), and provide the explicit Galois action ...
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: The Ramanujan Journal
سال: 2010
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-010-9249-y