Modular forms at cm points

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August undefined, 2024

WebModular form theory is a special case of the more general theory of automorphic forms which are functions defined on Lie groups which transform nicely with respect to the action of certain discrete subgroups, generalizing the example of the modular group . General definition of modular forms [ edit] Web13 okt. 2015 · The progress on modularity achieved in recent decades ensures the existence of normalized eigenforms f, g, and h of respective weights two, one, and one, giving rise to E, ϱ♭, and ϱ♯ via the constructions of …

On values of Modular Forms at Algebraic Points - 國立臺灣大學

http://math.columbia.edu/~yihang/CMTutorial/notes%209-25.pdf Webin the theory of modular forms, namely the study of congruences, which in its modern formulation, due to Hida, Ribet and ultimately in the work of Wiles and Taylor … presby mychart

Modular Functions and Special Cycles - uni-bonn.de

WebThe values of j(τ) at CM points are known as singular moduli. They are algebraic integers generating Hilbert class ﬁelds of imaginary quadratic ﬁelds. In this note we con-sider … Web3 jun. 2024 · In this setting, this predicts that non-CM forms of partial weight one should be rare. It might even be plausible to conjecture that, up to twisting, there are only finitely many such forms of fixed tame level. However, such conjectures are completely open, and Stubley’s result is one of the first general theorems which points in that direction. Web20 dec. 2005 · Iwaniec, H.: Fourier coefficients of modular forms of half-integral weight. Invent. Math. 87(2), 385–401 (1987) Article MathSciNet Google Scholar Iwaniec, H.: … scottish blend tea

Modular form - Wikipedia

WebIn Chapter 2 we compute the restriction of Siegel Eisenstein series of degree 2 and more generally of Saito-Kurokawa lifts of elliptic modular forms to Humbert varieties. Using these restriction formulas we obtain certain identities for special values of symmetric square L … Web27 feb. 2024 · At CM points the splittings \Psi _\infty and \Psi _p coincide, and therefore one deduces rationality results for the values of \Theta _ {p,r} at CM points from ( 2 ). For details, see [ 4, Proposition 1.12]. The p -adic Maass–Shimura operator is then used in [ 4, 26] to construct p -adic L -functions and study their properties. scottish blood donors appointment edinburghWebA CM point of His a point t 2Hwhich satisﬁes a quadratic equation over Q, so that t = a +b p d for some a,b,d 2Q with d < 0 and b > 0. Theorem 4. Let t 2H\Q(p d) (for some d < 0) … scottish blood donors appointment

"WebPower series expansions of modular forms at CM points 365 Consider the universal familyQM ^-^3^r and the shea =f u ^(^QM/A,). No w the fìbers of the universal family over … " - Modular forms at cm points

Modular forms at cm points

Webbe the modular j-function, where τ ∈H = {τ ∈C : Im(τ) >0}and q= e2πiτ. Then j aτ+b cτ+d = j(τ) for a b c d ∈SL 2(Z). If τ= u+ ivand u∈Q, v2 ∈Q, then τis an CM point. This is … WebReview of semisimple algebras and their modules 8;CM-algebras 10;CM-types. 11;The reﬂex ﬁeld of a CM-pair 13;The reﬂex norm. 14; ... related to that of the values of modular functions and modular forms at those points. The ﬁrst important result in the subject, which goes back to Kronecker and Weber,

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WebIt takes the following form. Fix a CM point ˝ 2H g in the Siegel upper half space, and let N be a positive integer. Assume that the CM-type of ˝ is primitive, and let r be its re ex. Let … Web13 feb. 2013 · There is a more down-to-earth definition. A newform f = ∑ n = 1 ∞ a n q n of level N and weight k has CM if there is a quadratic imaginary field K such that a p = 0 as …

WebThis also related to the previous work on evaluating modular forms at CM points. All this is just to say that even in the 19th century the subject was very deep, and already very … Webmodular forms, as opposed to the vector-valued forms ˜gand θΛ. See espe-cially Theorem 3.4.1. 1.3. Central derivatives and big CM points. Fix a totally real ﬁeld F of degree n, and deﬁne a CM ﬁeld E“ kbQF. Let Φ Ă HompE,Cq be a …

http://www.math.ntu.edu.tw/~yu/slidesoflectures/Macau%2010.pdf WebSpecial values of Drinfeld modular forms at CM points DavidAyotte Québec-Maine Number Theory Conferences Université Laval October15,2024

http://van-der-geer.nl/~gerard/schier06.pdf

WebAn Introduction to Modular Forms 3 T(a)= ∑ n∈Z e−aπn2. We have the functionalequation T(1/a)=a1/2T(a). Proof. Immediate from the propositionand Poisson summation. ⊓⊔ This … presby hymn 502WebModular forms of level one 2.1 Modular functions and forms Modular forms are holomorphic functions which transform in a speci ed way under the action of SL 2(Z) on the upper half plane H, and satisfy a growth property. We begin by de ning this action of SL 2(Z). 2.1.1 The action of SL 2(R) on H The elements of GL scottish bluebells flowersWeb2 feb. 2016 · In this paper, we study real-dihedral harmonic Maass forms and their Fourier coefficients. The main result expresses the values of Hilbert modular forms at twisted … presby hospital denton txWeb10 jan. 2024 · They are one of the most esoteric entities in mathematics, and yet the twentieth-century number theorist Martin Eichler rated them as one of the five … scottish blood serviceWebTo obtain the corollary, we use the theory of the Poincaré series and the method of quadratic twists to show first that a putative modular form must have weight 1/2. Corollary 1.2 then follows by applying Theorem 1.1. The paper is organized as follows. scottish blue ribbon songWebDIFFERENCE OF MODULAR FUNCTIONS AND THEIR CM VALUE FACTORIZATION TO APPEAR IN TRANS. AMS TONGHAI YANG AND HONGBO YIN Abstract. In this paper, … scottish bmdWeb1 feb. 2006 · Modular functions and the uniform distribution of CM points. February 2006; Mathematische Annalen 334(2):241-252; ... efﬁcient of an appropriate weight 3 / 2 … presby hospital map