The modular surface and quadratic forms
On congruences of modular forms over imaginary quadratic fields
... associated to some automorphic representation Π 0 of GSp(4, A Q ), such that R 0 | I p ∼ = τ p , for all p ∈ S. This is yet unproved, but as we discussed in Subsection 6.2.1, one hopes that Theorem 6.2.5 will be ...
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Euler systems for modular forms over imaginary quadratic fields
... different modular curves – can be “massaged” into an Euler system in the more conventional sense, a family of classes in the cohomology of one fixed Galois representation over varying extensions of the field ...
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A note on quadratic forms
... Crouzeix et al. [3] pointed out that Yuan’s result is actually an alternate theorem. They also extended Theorem 1 to a locally convex topological linear space. For any symmetric matrices C 1 and C 2 , Theorem 1 shows ...
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Quadratic points on modular curves
... over quadratic fields and similar Diophantine ...given quadratic field, K ...of quadratic points is useful in establishing irreducibility for small values of ...
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Annihilating polynomials for quadratic forms
... trace forms of finite separable field exten- sions because he believed that if one had some information about the Galois group of the field extension then an improvement on Theorem 2 was ...
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4. BINARY QUADRATIC FORMS
... binary quadratic form; and it is still of interest to determine which integers are represented by a given quadratic form in no matter how many ...which quadratic forms represent all ...a ...
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Spaces of modular forms. Modular curves and dimensions
... Before Wiles, (FLT) ` had been proved for all primes ` less than four million. Taniyama–Shimura conjecture On the other hand, in the middle of the 20th century, the Japanese mathe- maticians Yutaka Taniyama and Goro ...
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MAASS FORMS, MODULAR FORMS, AND REPRESENTATION THEORY
... The theory of root systems already shows from this that the raising and lowering operators are supposed to go between the weight spaces of weights differing by 2 without killing anything[r] ...
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Elliptic Modular Forms and Their Applications
... of modular forms of a given weight on Γ is finite dimen- sional and algorithmically computable, so that it is a mechanical procedure to prove any given identity among modular ...Secondly, ...
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On the critical points of modular forms
... each modular form, an equivariant function that commutes with the action of the modular ...every modular forms has infinitely many inequivalent zeros in the upper ...quasimodular forms ...
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Modular Forms and Invariant Theory
... So c vanishes with order 14 along the locus of double conics (confirms a result of Aluffi-Cuckierman).... In principle we can describe all modular forms of genus 3F[r] ...
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Saddlepoint approximations for noncentral quadratic forms
... of quadratic forms in normal variables+ Excepting a few very special cases little is known about the density or distribution of these ratios, particularly if we allow for noncentrality in the qua- dratic ...
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On types of local deformations of quadratic forms
... definite quadratic forms: if the matrix of a quadratic form has rank r and the first r corner minors are positive definite, then the quadratic form is non-negative ...
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Composition and characters of binary quadratic forms
... The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions.. Copyright © and all moral [r] ...
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The skew elliptical distributions and their quadratic forms
... In this paper, combining these two directions, we propose and study a family of the skew elliptical distributions, which includes the skew normal distributions in [4,5] , the skew elliptical distributions in [6] and a ...
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Sums of powers of binary quadratic forms
... We do not know how to completely characterize the sets of sums of three cubes for a given p and what other symmetries those sets might have. Clearly these tools from Ecole de calcul ad hoc ` will not generalize to higher ...
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ON THE FIRST WITT INDEX OF QUADRATIC FORMS
... Let X be the projective quadric over F given by an anisotropic quadratic form φ. We set d = dim(X) (that is, d = dim(φ) − 2) and assume that this integer is odd. Therefore, over an algebraic closure ¯ F of F , the ...
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Extremality and designs in spaces of quadratic forms
... definite quadratic forms on a finite- dimensional real vector space, and the high symmetry of that ground space which is expressed by the existence of a Lie group acting naturally and transitively on ...
CLASSIFICATION OF QUADRATIC FORMS OVER Q
... of quadratic forms with integer coef- ficients which intervenes in various questions related to modular forms, differential topology and finite ...of quadratic forms over Q p and ...
The connection of furniture through modular forms
... technology in the surf, skate and snowboard cultures, followed by a discussion of design techniques, forms a central part of this account. Furthermore, the influences provided by conte[r] ...
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