Modular Functions and Modular Forms
Modular functions obtained from modular polynomials
... A modular function is a meromorphic function on the upper half complex plane H which is also "meromorphic at the cusps" and invariant under the action on H of some matrix group Γ, called a "congruence ...
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Elliptic Modular Forms and Their Applications
... the modular forms arising from algebraic number theory or algebraic geometry whose L-series have Eu- ler ...of modular forms, and in particular the differential equations which these ...
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Contributions to the theory of modular forms and L-functions
... elliptic functions (see [29], Chapter ...simple functions which we will call weak ...weak functions with poles only in ...cusp forms of weight 2 ≤ k ≤ 14, k 6= 12, for the full modular ...
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The L functions and modular forms database project
... A related objects box on each home page provides links between related objects. For example, from the pages of an elliptic curve, or a number field, or a modular form there are links to the associated L-function. ...
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P adic L functions of Bianchi modular forms
... overconvergent modular symbols, Pollack and Stevens (see [19] and [20], or for an exposition, [18]) gave a beautiful and computationally effective method of constructing the p-adic L-function of a suitable rational ...
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Spaces of modular forms. Modular curves and dimensions
... Automorphic, modular and cusp forms In this second chapter we introduce the C-vector spaces of automorphic, modular and cusp ...introduction, modular forms play a special role in the ...
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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 ...equivariant functions with the aim that if such equivariant function is not the iden- tity, then the image ...
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Critical slope p adic L functions of CM modular forms
... ordinary modular forms, there are two constructions of a p-adic L- function attached to the non-unit root of the Hecke polynomial, which are conjectured but not known to ...for modular forms ...
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Interpolated Apéry numbers, quasiperiods of modular forms, and motivic gamma functions
... of modular forms and their entire theory worked out by Martin Eichler [7] in 1957, but were then forgotten and rediscovered some 60 years later by Francis Brown [4], [5] and also by us at about the same ...
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Rankin Eisenstein classes for modular forms
... Flach elements under r syn to the values of p-adic L-functions (for good ordinary primes p), a p-adic version of Beilinson’s computation of the Deligne regulators of these elements. 1.2. Outline of the paper. The ...
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Eigenvarieties associated to Hilbert modular forms
... Proof. This follows at once from the fact that the entries of the matrix are given by uniformly continuous functions and the coefficients of the characteristic polynomial are given as sums and products of these ...
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Slopes of Modular Forms and the Ghost Conjecture
... In this article, we present a unifying conjecture, which we call the ghost conjecture, that predicts the slopes of overconvergent p-adic cuspforms over all of p-adic weight space simultaneously. The shape of our ...
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One Dimensional Hurwitz Spaces, Modular Curves, and Real Forms of Belyi Meromorphic Functions
... p-fold functions with four branched points, three of them fixed; the corresponding monodromy representation over each branched point is a product of p − 1/2 transpositions and the monodromy group is the dihedral ...
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UNIMODAL SEQUENCES AND QUANTUM AND MOCK MODULAR FORMS
... holomorphic forms of half-integer weight which are congruent to cusp forms modulo ...cusp forms, which by Lemma ...cusp forms modulo ...
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Probabilities as Values of Modular Forms and Continued Fractions
... generating functions for p k n and mock theta functions and nonholomorphic modular ...a modular form and a Maass ...of modular forms and harmonic Maass forms to obtain ...
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Wach modules and Iwasawa theory for modular forms
... a n q n be a normalized new eigenform and p an odd prime at which f is either good ordinary or supersingular. By applying our theory to the p-adic representation associated to f, we define Coleman maps Col i for i = 1, 2 ...
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Modular identities for the Rogers-Ramanujan functions and analogues
... After the work of Rogers, Watson, and Bressoud, nine identities remained to be proved. A.J.F. Biagioli [24] used the theory of modular forms to prove eight of them; it is clear that modular ...
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BOUNDS FOR MODULAR L-FUNCTIONS IN THE LEVEL ASPECT
... of modular forms provides a natural spectral expansion of the Eisenstein spectrum in which the basis of Eisenstein series is indexed by a set of parameters of the form ...
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Euler systems for Rankin Selberg convolutions of modular forms
... We next turn to the relation between our elements and L-values. Theorem 4.3.7 shows, following an argument due to Beilinson, that the images of the elements c Ξ m,N,j under the Beilinson regulator map into complex de ...
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Bilateral series in terms of mixed mock modular forms
... 12. Chen, B, Zhou, HG: Note on the problem of Ramanujan’s radial limits. Adv. Differ. Equ. 2014, 191 (2014) 13. Bajpai, J, Kimport, S, Liang, J, Ma, D, Ricci, J: Bilateral series and Ramanujan’s radial limits. Proc. Am. ...
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