Add to ORKGCycle integrals of modular functions are expected to play a role in real quadratic analogue of singular moduli. In this paper, we extend the definition of cycle integrals of modular functions from real quadratic numbers to badly approximable numbers. We also give explicit representations of values of extended-cycle integrals for some cases.Comment: 19 pages, 4 figure
Here we study the integrality properties of singular moduli of a special non-holomorphic function γ(...
The Shimura correspondence connects modular forms of integral weights and half-integral weights. One...
This thesis intends to make a contribution to the theories of algebraic cycles and moduli spaces ove...
Yu. I. Manin conjectured that the maximal abelian extensions of the real quadratic number fields are...
In this paper, regularized Petersson inner products of certain weight weakly holomorphic (or harmoni...
Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss–Kuzmin theorem...
Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss–Kuzmin theorem...
A (folklore?) conjecture states that no holomorphic modular form $F(\tau)=\sum_{n=1}^\infty a_nq^n\i...
We prove modularity of formal series of Jacobi forms that satisfy a natural symmetry condition. They...
Let $K$ be an imaginary quadratic field where $p$ splits, $p\geq5$ a prime number and $f$ an eigen-n...
AbstractWe construct several rational period functions for modular integrals with weight 2k on the m...
It is well-known that the Ap\'ery sequences which arise in the irrationality proofs for $\zeta(2)$ a...
AbstractThe author has previously shown that there are exactly nine complex quadratic fields of clas...
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on ...
In this paper we give some applications of weakly holomorphic forms and their cycle integrals to rat...
Here we study the integrality properties of singular moduli of a special non-holomorphic function γ(...
The Shimura correspondence connects modular forms of integral weights and half-integral weights. One...
This thesis intends to make a contribution to the theories of algebraic cycles and moduli spaces ove...
Yu. I. Manin conjectured that the maximal abelian extensions of the real quadratic number fields are...
In this paper, regularized Petersson inner products of certain weight weakly holomorphic (or harmoni...
Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss–Kuzmin theorem...
Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss–Kuzmin theorem...
A (folklore?) conjecture states that no holomorphic modular form $F(\tau)=\sum_{n=1}^\infty a_nq^n\i...
We prove modularity of formal series of Jacobi forms that satisfy a natural symmetry condition. They...
Let $K$ be an imaginary quadratic field where $p$ splits, $p\geq5$ a prime number and $f$ an eigen-n...
AbstractWe construct several rational period functions for modular integrals with weight 2k on the m...
It is well-known that the Ap\'ery sequences which arise in the irrationality proofs for $\zeta(2)$ a...
AbstractThe author has previously shown that there are exactly nine complex quadratic fields of clas...
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on ...
In this paper we give some applications of weakly holomorphic forms and their cycle integrals to rat...
Here we study the integrality properties of singular moduli of a special non-holomorphic function γ(...
The Shimura correspondence connects modular forms of integral weights and half-integral weights. One...
This thesis intends to make a contribution to the theories of algebraic cycles and moduli spaces ove...