In mathematics, the theta divisor Θ is the divisor in the sense of algebraic geometry defined on an abelian variety A over the complex numbers (and principally...

In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic...

identification of theta divisors and translates of the curve C {\displaystyle C} . There is a 1-1 correspondence between pairs of odd symmetric theta divisors and 2-torsion...

In mathematics, a theta characteristic of a non-singular algebraic curve C is a divisor class Θ such that 2Θ is the canonical class. In terms of holomorphic...

nonsingular curve of genus ≥ 0 over k, and J its Jacobian, then the theta-divisor of J induces a principal polarisation of J, which in this particular...

van der Geer, G.; Schoof, R. (2000). "Effectivity of Arakelov divisors and the theta divisor of a number field". Selecta Mathematica. New Series. 6 (4):...

Riemann–Roch theorem in all its refinements (via the detailed geometry of the theta-divisor). The classification of algebraic surfaces was a bold and successful...

under addition on J (see theta-divisor) have dimension n and fill up J, with some identifications caused by special divisors. For g = n we have ΣgC actually...

correspondence between line bundles and divisors (built from codimension-1 subvarieties), there is an equivalent notion of a nef divisor. More generally, a line bundle...

{\displaystyle \sin ^{2}\theta +\cos ^{2}\theta =1.} As usual, sin 2 ⁡ θ {\displaystyle \sin ^{2}\theta } means ( sin ⁡ θ ) 2 {\textstyle (\sin \theta )^{2}} . Any...

N(d) of the greatest common divisor of a and b is a common divisor of N(a), N(b), and N(a + b). When the greatest common divisor D of these three integers...

number theory, σ is included in various divisor functions, especially the sigma function or sum-of-divisors function. In applied mathematics, σ(T) denotes...

deficiency" method, which says to "...combine the excess and deficiency as the divisor; (taking) the deficiency numerator multiplied by the excess denominator...

results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and...

) q 2 n {\displaystyle \Theta _{\Gamma _{8}}(\tau )=1+240\sum _{n=1}^{\infty }\sigma _{3}(n)q^{2n}} where σ3(n) is the divisor function. It follows that...

mathematics at the University of Liverpool, where she wrote "The divisor of curves with a vanishing theta-null", for Compositio Mathematica in 1988. In 1997, she...

_{0}^{\theta }\sin \theta '\,d\theta '\,d\phi &=\int _{0}^{2\pi }d\phi \int _{0}^{\theta }\sin \theta '\,d\theta '\\&=2\pi \int _{0}^{\theta }\sin \theta '\...

every finite semigroup S is a divisor of a finite alternating wreath product of finite simple groups (each of which is a divisor of S) and finite aperiodic...

\theta _{1}\cos \theta _{2}+\sin \theta _{1}\sin \theta _{2}\right)\\&=r_{1}^{2}+r_{2}^{2}-2r_{1}r_{2}\cos \left(\theta _{1}-\theta...

frontotemporal lobar degeneration, and chronic traumatic encephalopathy Divisor function in number theory, also denoted d or σ0 Ramanujan tau function...

over M g , 1 {\displaystyle {\mathcal {M}}_{g,1}} , by Yin. Powers of theta-divisor on the universal abelian variety, by Grushevsky and Zakharov. These...

1016/B978-0-12-067570-8.50031-7. Patterson, S. J.; Perry, Peter A. (2001). "The divisor of Selberg's zeta function for Kleinian groups". Duke Mathematical Journal...

S={\begin{bmatrix}\cos \theta &-\sin \theta &0\\\sin \theta &\cos \theta &0\\0&0&1\end{bmatrix}},} where θ {\displaystyle \theta } is the angle of rotation...

is Riemann's zeta function and σp(n) is the divisor sum function, the sum of the pth powers of the divisors of n. In particular, one has G 4 ( τ ) = π...

z=\rho e^{i\theta }=\rho (\cos \theta +i\sin \theta ),} where ρ {\displaystyle \rho } is the absolute value of z, and θ {\displaystyle \theta } is its argument...

where d1(n) is the number of divisors of n which are congruent to 1 modulo 4 and d3(n) is the number of divisors of n which are congruent to 3 modulo...

an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n. Arithmetic functions are...

{\displaystyle p_{n+1}-p_{n}<p_{n}^{\theta },} for all sufficiently large n. Huxley also improved the known bound on the Dirichlet divisor problem. In 2011, Huxley...

2^{k}} divisors. For example, 2 # {\displaystyle 2\#} has 2 divisors, 3 # {\displaystyle 3\#} has 4 divisors, 5 # {\displaystyle 5\#} has 8 divisors and...

= cos ⁡ n θ + i sin ⁡ n θ {\displaystyle (\cos \theta +i\sin \theta )^{n}=\cos n\theta +i\sin n\theta } while Euler's formula of complex analysis (1748)...