elliptic curves and topological modular forms

... sense that for all i and j, #(αi ∩ γj ) = δi,j (the right-hand side is Kronecker delta, and the left-hand side denotes both the geometric and algebraic intersection numbers of the curves) By isotoping ... both the αt and the β t are g-tuples of smoothly embedded, pairwise disjoint curves We say that (Σ , α , β ) is obtained from (Σ, α, β) by handleslides if Σ = Σ and α are obtained by handleslides ... diffeomorphic copy of the domain Di The α -curves are divided up by the β -curves into subsets, which we call α-arcs; and similarly, the β -curves are divided up by the α -curves into β-arcs Each α or β-arc...

Ngày tải lên: 05/03/2014, 23:20

... 1–64 Iwasawa’s Main Conjecture for elliptic curves over anticyclotomic Zp-extensions By M Bertolini∗ and H Darmon∗* Contents p-adic L-functions 1.1 Modular forms on quaternion algebras 1.2 p-adic ... number Elliptic curves If E is an elliptic curve as in the introduction, let fE be the modular form in S2 (T /Γ) attached to it by Proposition 1.4 The p-adic L-function attached to E and K is ... ) ∗( ) and H (Q , Wf ) are orthogonal to each other under the local Tate pairing 25 IWASAWA’S MAIN CONJECTURE FOR ELLIPTIC CURVES Proposition 3.6 The modular form f is p-isolated if and only...

Ngày tải lên: 06/03/2014, 08:21

... lemmas are easily established and relatively standard, see [19], [25] and [6, §7] A.1.2 Positive and full measure sets Proposition Let E ⊂ R be a measurable set and let I0 ⊂ R be an interval ... VICTOR BERESNEVICH, DETTA DICKINSON, AND SANJU VELANI Step In view of Steps and above, the function ψ satisfies (4) and Corollary is applicable to ψ By (27) and the fact that ψ is decreasing, we ... Theorems and Corollary Let ψ and f be as in Theorem and C := {(x, f (x)) : x ∈ I0 } With reference to the ubiquitous framework of §3.2, set (11) β : J := Z2 × N → N : (p, q) → q , Φ : t → t−1 ψ(t) and...

Ngày tải lên: 15/03/2014, 09:20

... Cusp forms and Poincare series Non-cusp forms IV Small weights Singular modular forms and theta-series The graded ring of modular forms of degree two V Modular functions 10 11 VI Quotients of modular ... The modular group The symplectic group Minkowski's reduction theory Fundamental sets of Siegel's modular group Basic facts on modular forms The linear space of modular forms Eisenstein series and ... modular forms, or found similar types of functions such as Hermitian modular forms, Hilbert-Siegel modular forms, or recently modular forms on half-spaces of quaternions The need for a unified comprehensive...

Ngày tải lên: 22/03/2014, 15:20

... setting and notation are laid out in Section Sections and describe the classical and Kobayashi Selmer groups, and Sections and relate Kobayashi’s construction to local units, elliptic units, and ... conjecture for elliptic curves with complex multiplication Introduction Iwasawa theory was introduced into the study of the arithmetic of elliptic curves by Mazur in the 1970’s Given an elliptic curve ... proof relies on the Euler system of elliptic units, and the results and methods of [Ru3] which also went into the proof of the main conjecture for CM elliptic curves at ordinary primes We sketch...

Ngày tải lên: 28/03/2014, 22:20

... 168 Elliptic curves over C 170 172 Elliptic curves over local fields 178 Elliptic curves over number fields Elliptic curves with complex ... characteristics and elliptic curves, Proc Nat Acad Sci USA 94 (1997), 11115-11117 J Coates, S Howson, Euler characteristics and elliptic curves 11, in preparation J Coates, R Sujatha, Galois cohomology of elliptic ... arithmetic of elliptic curves consists in the study of modularity properties of elliptic curves over Q, or of the structure of the Mordell-Weil group E ( K ) of K-rational points on an elliptic curve...

Ngày tải lên: 31/03/2014, 16:21

... Forms Definition of a modular form The modular forms for Γ0 (1) 125 26 Modular Forms and the L-series of Elliptic Curves Dirichlet Series The L-series of an elliptic curve L-series and isogeny classes ... become visible in the study elliptic curves, and elliptic curves have been used solve some very famous problems that, at first sight, appear to have nothing to with elliptic curves I mention three ... through through through through P and Q; Q and R; O and P Q; O and QR; P + Q and R; Q + R and P [[diagram omitted]] Let S = (P + Q)R, T = P (Q + R) Then (P + Q) + R = OS and P + (Q + R) = OT We shall...

Ngày tải lên: 31/03/2014, 16:21

... Semistable Curves and Tate Modules The Frey Curve and the Reduction of Fermat Equation to Modular Elliptic Curves over Q Modular Elliptic ... Real and Complex Points on Elliptic Curves 19 §7 Real and Complex Points on Elliptic Curves Let E be an elliptic curve over the real or complex numbers The structure of the groups E(R) and E(C) ... Rational Cubics and Mordell’s Theorem The Group Law on Cubic Curves and Elliptic Curves Rational Points on Rational Curves Faltings and the Mordell Conjecture...

Ngày tải lên: 31/03/2014, 16:22

... investigated/optimized, and then the arrangement and geometry (width, height, and length) of the TEMs are varied within prescribed bounds to compute outputs such as the electrical power and associated ... for hexagonal (blue) with DO = 0.105 m and DI = 0.04 m and cylindrical (red) with DO = 0.08 m and DI = 0.04 m models for pure skutterudite (solid line) and hybrid (dashed line) arrangements with ... generation and associated pressure drop is presented for a fixed geometry and heat exchanger topology In this section, the influence of parameters such as the heat exchanger design (number of fins and...

Ngày tải lên: 06/05/2014, 08:54

... investigated/optimized, and then the arrangement and geometry (width, height, and length) of the TEMs are varied within prescribed bounds to compute outputs such as the electrical power and associated ... for hexagonal (blue) with DO = 0.105 m and DI = 0.04 m and cylindrical (red) with DO = 0.08 m and DI = 0.04 m models for pure skutterudite (solid line) and hybrid (dashed line) arrangements with ... generation and associated pressure drop is presented for a fixed geometry and heat exchanger topology In this section, the influence of parameters such as the heat exchanger design (number of fins and...

Ngày tải lên: 06/05/2014, 08:58

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Ngày tải lên: 29/06/2014, 10:22

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 10:20

... fixed positions i and j correspond to the intersection of two planes, and so on Hence, two code words w1 and w2 corresponding to the affine points P and Q will have t common entries if and only if the ... q) and let E = Σ \ Π The code C can be extended if and only if there exists a partition {X1 , X2 , , Xq } of E where each Xi is a transversal set of T Geometry and Combinatorics of Cubic Curves ... #R42 [6] J W P Hirschfeld and J F Voloch The characterization of elliptic curves over finite fields J Austral Math Soc Ser A, 45(2):275–286, 1988 [7] Fred Lang Geometry and group structures of some...

Ngày tải lên: 07/08/2014, 15:23

... OF CLASSICAL MODULAR FORMS TO NUMBER THEORY Committee: Fernando Rodriguez-Villegas, Supervisor David Boyd Sean Keel David J Saltman John Tate SOME APPLICATIONS OF CLASSICAL MODULAR FORMS TO NUMBER ... MODULAR FORMS TO NUMBER THEORY Publication No Riad Mohamad Masri, Ph.D The University of Texas at Austin, 2005 Supervisor: Fernando Rodriguez-Villegas In this thesis we use classical modular forms ... with Re(s) > 2, and f (w) = δij (y (j) )s + O(1) as y (j) → ∞, then f (w) = Ei (w, s) ˜ Efrat and Sarnak [ES] showed that Ei (w, s) satisfies conditions and of ˜ Lemma 3.2.8, and hence that Ei...

Ngày tải lên: 13/11/2014, 09:14

Ngày tải lên: 13/11/2014, 10:55

... Jiangwei and Li Xikun for making cheerful office environment Last but not least, I would like to thank my girlfriend Tao Lu and my parents Thanks for their whole-hearted supports and kind understandings ... potentials For weak and strong interactions in the standard model, forces are mediated by more complicated gauge fields They follow from a local SU (2) and SU (3) gauge invariance theory, and their force ... state level and driven by resonant 1-photon transitions Using an appropriate combination of four Laguerre-Gauss and two Hermite-Gauss laser beams, we are able to produce a U (3)-monopole and a U...

Ngày tải lên: 09/09/2015, 08:12

... splitting in both graphene and BiTeI’s bands (see Figure 3.8(b)) In addition, the Fermi level crosses the conduction band and the valence band at G and K, respectively These two bands are separately ... due to the interaction between top and bottom surfaces, and moreover, linear Dirac bands and massless fermions are replaced by conventional parabolic bands and massive fermions [4, 28, 29] For ... vanishes and an energy gap appears Chapter Introduction Another intriguing effect in TI is topological phase transition characterized by the parity exchange between conduction bands and valence bands...

Ngày tải lên: 30/09/2015, 10:12