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1
Content available remote

Tate-Shafarevich groups of the congruent number elliptic curves

100%
Acta Arithmetica
|
1997
|
tom 81
|
nr 3
247-252
2
Content available remote

On the positivity of the number of t-core partitions

100%
Acta Arithmetica
|
1994
|
tom 66
|
nr 3
221-228
EN
A partition of a positive integer n is a nonincreasing sequence of positive integers with sum $n.$ Here we define a special class of partitions. \de{1.} Let $t ≥ 1$ be a positive integer. Any partition of n whose Ferrers graph have no hook numbers divisible by t is known as a t- core partition} of $n.$ \vskip 4pt plus 2pt The hooks are important in the representation theory of finite symmetric groups and the theory of cranks associated with Ramanujan's congruences for the ordinary partition function [3,$\,$4,$\,$6]. If $t≥ 1$ and $n ≥ 0$, then we define $c_t(n)$ to be the number of partitions of n that are t-core partitions. The arithmetic of $c_t(n)$ is studied in [3,$\,$4]. The power series generating function for $c_t(n)$ is given by the infinite product: ∑_{n=0}^{∞} c_t(n)q^n= \prod_{n=1}^{∞
3
Content available remote

Euler's concordant forms

100%
Acta Arithmetica
|
1996-1997
|
tom 78
|
nr 2
101-123
4
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4-core partitions and class numbers

64%
Acta Arithmetica
|
1997
|
tom 80
|
nr 3
249-272
5
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Identities for traces of singular moduli

64%
6
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Gauss's ₂F₁ hypergeometric function and the congruent number elliptic curve

64%
7
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Divisibility criteria for class numbers of imaginary quadratic fields

64%
8
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Arithmetic of certain hypergeometric modular forms

64%
9
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The arithmetic of the coefficients of half-integral weight Eisenstein series

51%
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