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MODULAR CURVES AND RAMANUJAN’S CONTINUED FRACTION
modular curve Ramanujan continued fraction
2015/7/6
We use arithmetic models of modular curves to establish some properties of Ramanujan’s continued fraction. In particular, we give a new geometric proof that its singular values are algebraic units
th...
Modular Equations and Evaluations of Ramanujan Quantities
Ramanujan Continued Fractions Quantities Modular Equations Derivatives Evaluations
2011/9/5
Abstract: In this article we continue a previous work, in which we have generalized the Rogers Ramanujan continued fraction (RR) introducing what we call, the Ramanujan-Quantities (RQ). In the present...
Iwasawa Theory for the Symmetric Square of a CM Modular Form at Inert Primes
Iwasawa Theory Symmetric Square CM Modular Form
2011/1/19
Let f be a CM modular form and p an odd prime which is inert in the CM field. We construct
two p-adic L-functions for the symmetric square of f, one of which has the same interpolating properties as ...
Mass equidistribution of Hilbert modular eigenforms
Mass equidistribution Hilbert modular eigenforms
2010/11/11
Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show th...
Eisenstein Series, Alternative Modular Bases and Approximations of $1/\pi$
Eisenstein Series Alternative Modular Bases
2010/11/22
In this article using the theory of Eisenstein series, we give rise to the complete evaluation of two Gauss hypergeometric functions. Moreover we evaluate the modulus of each of these functions and t...
Quasi-modular forms attached to Hodge structures
Polarized Hodge structure Griffiths transversality
2010/12/13
The space D of Hodge structures on a fixed polarized lattice is known as Griffiths period domain and its quotient by the isometry group of the lattice is the moduli of polarized Hodge structures of a ...
On the cohomology groups of local systems over Hilbert modular varieties via Higgs bundles
cohomology groups of local systems Hilbert modular varieties Higgs bundles
2010/12/3
Let X be a Hilbert modular variety and V a non-trivial local system over X. In this paper we study Deligne-Saito’s mixed Hodge structure (MHS) on the cohomology groups Hk(X, V) using the method of Hig...
We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modul...