The series $heta (q,x):=\\sum _{j=0}^{\\infty}q^{j(j+1)/2}x^j$ converges for\n$q\\in [0,1)$, $x\\in \\mathbb{R}$, and defines a {\\em partial theta function}.\nFor any fixed $q\\in (0,1)$ it has infinitely many negative zeros. For $q$\ntaking one of ...
Z(t)Z(t). TheHardy Z functionis a continuous, real-valued function that takes a positive real numberttas its input and outputs a real number that can be either positive or negative. SinceZ(t)Z(t)is continuous, if it is positive (negative) at the beginning of a real int...
Let’s fix \(p~:~\mathbb {R}^2\rightarrow \mathbb {R}\) a linear map such that \(\ker (p)\cap \dot{\mathbb {R}}^2_+\ne \{0\}\) (i.e., such that the zeros of p are the graph of an increasing linear function). The keystone of our proof is the following proposition...
On the exact location of the non-trivial zeros of Riemann's zeta function In this paper we introduce the real valued real analytic function kappa(t) implicitly defined by exp(2 pi i kappa(t)) = -exp(-2 i theta(t)) * (zeta'(1/2-it... JAD Reyna,JVD Lune - 《Acta Arithmetica》...
On the zeros of Riemann $\\Xi(z)$ function Here heta(x):=heta_3(0,ix) heta(x):=heta_3(0,ix) and heta_3(0,z) heta_3(0,z) is a Jacobi theta function, a modular form of weight \\frac{1}{2} \\frac{1}{2} . (A) We discover a family of functions \\{... Y Shi ...
Your function has no dependence on var because x, y are defined outside the function. This would give the desired output instead: theta = np.pi/4 r = 4.0 var = np.array([r, theta]) def f(var): x = var[0]*jnp.cos(var[1]) y = var[0]*jnp.sin(var[1]) return jnp.array...
weighted Szegő kernel of McCullough and Shen but the weight parameterris changed depending on the added zeros. We also prove that the zero point process of the GAF provides a permanental-determinantal point process (PDPP) in which each correlation function is expressed by a permanent multiplied...
zeros(theta.shape), theta, z)), self) pt1.redefine(self._origin) vecin = vecin.split() x_hat = self + pt1 #creates a vector which includes all the centers of the subsurface out = [] #this for loop makes me cringe super hard for i in xrange(meri): try: temp = [] for j ...
BN Khabibullin - 《Mathematical Notes of the Academy of Sciences of the Ussr》 被引量: 6发表: 1988年 On the conditions for entire functions related to the partial theta function to belong to the Laguerre-Pólya class In this paper, we study entire functions of order zero with positive Taylo...
def computeNumericalGradient(J,theta): # numgrad = computeNumericalGradient(J, theta) # theta: a vector of parameters # J: a function that outputs r. # Calling y = J(theta) will return the function value at theta. # Initialize numgrad with zeros numgrad = np.zeros(np.shape(theta)...