[PDF] Top 20 Elliptic Modular Forms and Their Applications
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Elliptic Modular Forms and Their Applications
... “elliptic”) modular forms are functions in the complex upper half-plane which transform in a certain way under the action of a discrete subgroup Γ of SL(2, R ) such as SL(2, Z ...of modular ... See full document
103
The L functions and modular forms database project
... Hilbert modular forms were computed (in Magma ) by John Voight (Dartmouth College) and Steve Donnelly (Sydney) [7], while the elliptic curves were computed (in SageMath ) by Jonathan Bober (Bristol), ... See full document
14
Integer Factorization of Semi Primes Based on Analysis of a Sequence of Modular Elliptic Equations
... There are several algorithms that factorize a semi- prime n=pq, where n is known, but its integer factors p and q are not. Fermat, Euler and other mathemati- cians/computer scientists introduced various algorithms for ... See full document
7
Eigenvarieties associated to Hilbert modular forms
... such modular forms of a fixed level and their points correspond to systems of Hecke eigenvalues of finite slope overconvergent modular ...many applications such as in the proof of the ... See full document
137
P adic L functions of Bianchi modular forms
... non-CM elliptic curves over number ...overconvergent modular symbols, Pollack and Stevens (see [19] and [20], or for an exposition, [18]) gave a beautiful and computationally effective method of constructing ... See full document
43
Rankin Eisenstein classes for modular forms
... Thirdly, we use our computations of syntomic and Deligne regulators to verify an instance of a very general conjecture of Perrin-Riou, which roughly says that the leading terms of the complex L-functions at all integers ... See full document
37
On Level One Cuspidal Bianchi Modular Forms
... an elliptic curve defined over Q( √ − 643), and not over Q, which has everywhere good reduction and it should be ...an elliptic curve over Q ( √ − 643) and it does seem to be modular, see Scheutzow ... See full document
17
Modular Subgroups, Dessins d’Enfants and Elliptic K3 Surfaces
... associated modular forms ...the elliptic j-invariants of the Weierstraß models for the modular surfaces with base P 1 and we will complete this story in the present ... See full document
44
On the Tamagawa Number Conjecture for motives attached to modular forms
... We remark that, for all f , the module Z (f, T ) just defined really is the module that appears in the statement of the Main Conjecture. When f has CM, one prefers to work with elements coming from elliptic units, ... See full document
80
Wach modules and Iwasawa theory for modular forms
... supersingular elliptic curve). Using ideas of Kobayashi for elliptic curves which are supersingular at p, we associate to each of these power series a Λ-cotorsion Selmer ... See full document
46
Quantifying Regional-Scale Water Storage Using Models and Observations: Application For Drought Assessment In South Carolina
... For example, one may recast important results of Bump, Friedberg, and Hoff- stein, of Iwaniec, of Murty and Murty, and of Waldspurger, on non-vanishing of central critical L-values of quadratic twists of elliptic ... See full document
65
Hilbert modular forms of weight 1/2
... In Chapter 5 we define the congruent number problem over F and we take a few steps towards generalizing Tunnell’s results over Q. Here the generalization is not trivial, since already for Q( √ 2) there are examples of Q( ... See full document
45
Uniformization of modular elliptic curves via p-adic periods
... given elliptic curve is modular by a given ...to modular forms (see the recent breakthroughs [Sch13, HLTT13]) and the Faltings–Serre method (see [Liv87, ... See full document
33
A correspondence of modular forms and applications to values of L series
... In [7], Zudilin outlines a method he developed with M. Rogers on which their proof of Boyd’s conjectures is based. Here we reinterpret that method in terms of a correspon- dence of modular forms which is of ... See full document
12
Theta lifts of Bianchi modular forms and applications to paramodularity
... Secondly, we combine our lift with explicit computations of Bianchi modular forms to exhibit an abelian surface B defined over Q , which satisfies Conjecture 1.1 but is not a restriction of scalars of an ... See full document
18
Exceptional zeros and L invariants of Bianchi modular forms
... an elliptic curve over F. In this situation, the elliptic curve will have multiplicative reduction at p, so there is a Tate uniformiser q ∈ F p × such that E(F p ) ∼ = ... See full document
37
An Efficient Hardware Implementation of Finite Field Inversion for Elliptic Curve Cryptography
... The modular inversion operation is an essential hardware design for computing speed when we use it in cryptography ...high-performance modular binary inversion algorithm over 256-bit prime ... See full document
6
Reducing the Complexity of Normal Basis Multiplication
... There are essentially two categories of algorithms, based on the representation of field elements using polynomial basis or normal basis. In this paper, a new transformation method and a new multiplication algorithm for ... See full document
18
Bilateral series in terms of mixed mock modular forms
... mock modular form. The function f (q) is called a mixed mock modular form if it is the product of a modular form and a mock theta ...mock modular form are associated with the Ramanujan mock ... See full document
12
Efficient Hardware Implementation of Modular Arithmetic and Group Operation Over Prime Field
... The flow chart for the modular addition operation is presented in Figure 1(a). According to the algorithm, two inputs x and y are added. The intermediate result (x + y) could become greater than the predetermined ... See full document
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