Fricke involution

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August undefined, 2024

WebJul 21, 2024 · In this final section, we will prove the reciprocity laws Theorem 2.1 and Corollary 2.3 using the quantum modularity for the Fricke involution of additive twists proved above. 5.1 Proof of Theorem 2.1 and Corollary 2.3. By combining Corollary 3.3 and Theorem 4.8 with $r=-q/(lN)$, we get an explicit formula for the left-hand side of .

A note on additive twists, reciprocity laws and quantum ... - Springer

http://www.math.chalmers.se/~sj/forskning/eulerProdExpMath.pdf WebThe Fricke involution WN of level N, also known as the canonical involution, acts on the space of newforms of level N, some integral weight k, and trivial character. Here k is … grommet top curtain shower blossoms yellow

On the parity of the index of ramified Heegner divisors

WebThe modular curve X 0 + (p) = X 0 (p) / w p, where w p is the Fricke involution of X 0 (p), has genus zero. Every supersingular elliptic curve in characteristic p can be defined over the prime subfield F p. The order of the Monster group is divisible by p. The equivalence is due to Andrew Ogg. WebOct 18, 2014 · (In the case of half-integral weight, the Fricke involution is H M = H 4N in our notation.) Therefore, we will have an extra factor, which we call λ f. Note that the extra factor corresponding to the eigenvalues under H M also appears in Raghuram’s results (see ). Since normalization of Fourier coefficients is not known in the case of half ... WebDec 22, 2024 · In mathematics, a Fricke involution is the involution of the modular curve X 0 (N) given by τ → –1/Nτ. It is named after Robert Fricke. The Fricke involution also … files hidden on pc

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WebMar 1, 2024 · (p) consisting of all eigenforms of the Fricke involution W p with eigenvalue −1. We are interested in finding a canonical basis for the minus space M k! − (p) for certain levels. Using this result, along with previous works of Choi and Kim [CK13], we find a canonical basis for the space M k! WebThere are two definitions of the supersingular primes: one group-theoretic, and the other number-theoretic. Group-theoretically, let be the modular group Gamma0, and let be the compactification (by adding cusps) of , where is the upper half-plane . Also define to be the Fricke involution defined by the block matrix . For a prime, define . grommet top insulated curtainsWebthe Fricke involution ( I O1) Then, both rug(z) and i1g(z) are eigenforms for all Hecke operators if, and only if, g is one of the formal products listed in the second column of Table I. In particular this proves the existence of only a finite number of such il-quotients. Of these, not all are cusp forms or are invariant under the corresponding ... grommet textured curtains

"WebAug 15, 2013 · Eigenvalue of Fricke involution on newforms of level 4 and of trivial character. Yichao Zhang. In this note, we consider the newforms of integral weight, level … " - Fricke involution

Fricke involution

Algebraic hypergeometric transformations of modular origin

WebGalois representations attached to Q-curves and the generalized Fermat equation A4 +B2 = Cp Jordan S. Ellenberg ∗ Princeton University [email protected] WebThe second matrix is a Fricke involution. In general level N, the Fricke involution is W N:= 1 p N (0 1 N 0): The subgroup of (1) generated by 0(N) and the Fricke involution has a …

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Web0 (N) associated to the Fricke involution wN. Suppose φ is deﬁned over the rationals. In this note we give some collinearity relations among rational points of C, for each X+ 0 (N) of genus 3 and the ﬁrst X + 0 (N) of genus 4, for N prime. Contents 1. Introduction 1 2. Preliminaries 1 3. The relations 6 4. Concluding remarks 11 References ... In mathematics, a Fricke involution is the involution of the modular curve X0(N) given by τ → –1/Nτ. It is named after Robert Fricke. The Fricke involution also acts on other objects associated with the modular curve, such as spaces of modular forms and the Jacobian J0(N) of the modular curve.

Web0(q) by the Fricke involution z→ −1/qzwhen q= 24m− 1 is prime. In this case the genus of X∗ 0 (q)ism−(h−1)/2. Corollary. For q = 24m− 1 prime,the space of differential forms of the ﬁrst kind on X∗ 0 Web4 is the Fricke involution. We note that even if f is a Hecke eigenform, in general L(f,s) has no Euler product. Though L(f,s) has turned out to be useful in the investigation of sign changes of the coeﬃcients ℜ(a(n)) resp. ℑ(a(n)) [6], in general otherwise its meaning remains a bit mysterious.

Web4 is the Fricke involution. We note that even if f is a Hecke eigenform, in general L(f,s) has no Euler product. Though L(f,s) has turned out to be useful in the investigation of sign … WebAug 3, 2024 · On GL(2), the Fricke involution is well-known and is a special case of Atkin-Lehner-Li operator. nt.number-theory; gr.group-theory; modular-forms; automorphic …

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WebThe hyperelliptic involution s N →−s N will be the Fricke involution w N.The function ﬁeld of X 0(N) will be generated by t N,s N; and like s N, the Haupt-modul x N of X 0(N) will be a two-valued algebraic function of t N. This article will focus on the especially interesting case N = N2.When N =2,3,4, or 6, the automorphism group Γ 0(N2 ... grommet top curtains 84WebThe following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution. $277$ Dim. file shipsurance claimWebDec 23, 2015 · The U.S. Department of Energy's Office of Scientific and Technical Information grommet top fabric shower curtainWebAbstract. In [4], W. Kohnen constructed explicit Shintani lifts from the space of cusp forms of weight 2k 2 k on Γ0(N) Γ 0 ( N), which are mapped into the plus space S+ k+1/2(Γ0(4N)) S k + 1 / 2 + ( Γ 0 ( 4 N)), where N N is an odd integer. This lifting is adjoint to the (modified) Shimura map defined by him with respect to the Petersson ... file shirt robloxWebThe Fricke involution is the Atkin-Lehner involution w_N wN on the space S_k (\Gamma_0 (N)) Sk(Γ0(N)) (induced by the corresponding involution on the modular … files - home sharepoint.comWebFricke or Atkin Lehner involution : wN $ 0 1 N 0 Fact : wN normalizes 0(N) and 1(N) : wN a b Nc d w 1 N = d c Nb a Remark 3. wN does not commute in general with the action of T … file should be name xxx.cbpWebWe give a new, simpler proof that the canonical actions of finite groups on Fricke-type Monstrous Lie algebras yield genus zero functions in Generalized Monstrous Moonshine, using a Borcherds-Kac-Moody Lie algebra deco… file shortcut to desktop