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Results tagged with nt.number-theory
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user 49340
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
7
votes
1
answer
181
views
(Binary) Theta functions and Atkin's U-operator
Let $D<0$ be a fundamental discriminant and consider the theta series $$\vartheta_Q(\tau)=\sum_{v\in\mathbb{Z}^2} q^{Q(v)}$$
associated to a quadratic form $Q$ of discriminant $D$. It appears to be tr …
- 189
6
votes
1
answer
426
views
Asymptotic expansion of the Mordell integral
my question concerns the Mordell integral
$$h(z;\tau):=\int_{-\infty}^\infty \frac{e^{\pi i\tau w^2-2\pi zw}}{\cosh(\pi w)}dw,\qquad \Im(\tau)>0,\quad z\in\mathbb{C},$$
which frequently occurs in the …
- 189
2
votes
1
answer
225
views
2-parts of class numbers of binary quadratic forms for non-fundamental discriminants
I need a formula for the 2-adic valuation of the number of proper equivalence classes of primitive positive definite binary quadratic forms of discriminant $-D$, call it $h_0(-D)$. I'm sure the answer …
- 189