4. Weierstrass’s functions and modular forms Here we collect formulas which we need in the main text. Proofs (in slightly different notations) can be found in [6], [13]. Let τ∈ℂ be a modular parameter, we
We discuss how to build a zeta function for Drinfeld modules and introduce a symmetric group discovered by Thakur and Diaz-Vargas. An element in the symmetric group is essentially a set permutation of the p-adic integers. It is suspected that there is a relationship between this group and ...
B. Dwork. On the rationality of the zeta function of an algebraic variety. Amer. J. Math., 82:631–648, 1960. Article MathSciNet MATH Google Scholar H. M. Edwards. A normal form for elliptic curves. Bull. Amer. Math. Soc. (N.S.), 44(3):393–422 (electronic), 2007. Google...
Elliptic Curve (E): 1. Every E(Q) over Q is Modular 2. Δ = -16(4A³ + 27B²) Elliptic Curve Modular Form April 21, 2013tomcircle Modern Math Leave a comment Modular Form (MF): Is a function which takes Complex numbers from the upper half-plane as inputs and gives Complex...
This Eisenstein series is not a modular form, but the function ⁎E2⁎(z)=E2(z)−3/ϖy is non-holomorphic modular form. Since the Ramanujan-Serre operator is also expressed as ⁎ϑk=∂k−kE2⁎/12, we see that ϑk maps a modular form of weight k to a ...
The function f +(z) = n −∞ c+(n)qn is the holomorphic part of f (z), and its complement f −(z) is its non- holomorphic part. If f − = 0, then f = f + is a weakly holomorphic modular form. If f − is nontrivial, then f + is called a mock modular form. ...
1)elliptic function椭圆函数 1.By using the elliptic function and conformal transformation theory,a close form solution to this problem is obtained.运用椭圆函数和保角变换理论,获得了该问题严格的闭合解。 2.Phase plane properties of an electron in Wiggler field are analysed by using Jacobian elliptic ...
egg-shaped,elliptical,oval,oval-shaped,oviform,ovoid,prolate,ovate rounded- curving and somewhat round in shape rather than jagged; "low rounded hills"; "rounded shoulders" 3.elliptic- characterized by extreme economy of expression or omission of superfluous elements; "the dialogue is elliptic and...
3) liptic modular function field 椭圆模函数域 4) elliptic function 椭圆函数 1. By using theelliptic functionand conformal transformation theory,a close form solution to this problem is obtained. 运用椭圆函数和保角变换理论,获得了该问题严格的闭合解。
An elliptic integral is an integral of the form (1) or (2) where , , , and are polynomials in , and is a polynomial of degree 3 or 4. Stated more simply, an elliptic integral is an integral of the form (3) where is a rational function of and , is a function of ...