There is a class of remarkable series for 1/π of the form [formula could not be replicated] where A, B, C are certain algebraic numbers. These were first examined by Ramanujan. These examples arise by computing singular invariants for j and the constants involved will have degree equal to the class number of the associated imaginary quadratic field. Our intention is compute all such class number three examples. The largest such example, with discriminant −907, adds 37 additional digit accuracy per term. A class number four example with discriminant −1555 gives 50 digits per term
We resolve a family of recently observed identities involving 1/π using the theory of modular forms ...
AbstractIn this paper, we give parametric families of both real and complex quadratic number fields ...
Improving a result of Montgomery and Weinberger, we establish the existence of infinitely many real ...
AbstractThere is a class of remarkable series for 1/π of the form −C3π=∑n=0∞A+nBC3n (6n)(3n)(n)3 whe...
AbstractIn this article, we construct a general series for 1π. We indicate that Ramanujan's 1π-serie...
Many series for 1/π were discovered since the appearance of S. Ramanujan’s famous paper “Modular equ...
We compute Ramanujan–Sato series systematically in terms of Thompson series and their modular equati...
AbstractUsing certain representations for Eisenstein series, we derive several of Ramanujan's series...
In this paper, we use the explicit Shimura Reciprocity Law to compute the cubic singular moduli α∗n,...
In 1914 S. Ramanujan recorded a list of 17 series for 1/π. We survey the methods of proofs of Ramanu...
ABSTRACT Srinivasa Ramanujan had established several hypergeometric series for the number 1/π out of...
96 pages including large numerical tables and PARI programsSome PARI programs have bring out a prope...
AbstractIn this paper our attempt is to investigate the class number problem of imaginary quadratic ...
We outline an elementary method for proving numerical hypergeometric identities, in particular, Rama...
The class number problem is one of the central open problems of algebraic number theory. It has long...
We resolve a family of recently observed identities involving 1/π using the theory of modular forms ...
AbstractIn this paper, we give parametric families of both real and complex quadratic number fields ...
Improving a result of Montgomery and Weinberger, we establish the existence of infinitely many real ...
AbstractThere is a class of remarkable series for 1/π of the form −C3π=∑n=0∞A+nBC3n (6n)(3n)(n)3 whe...
AbstractIn this article, we construct a general series for 1π. We indicate that Ramanujan's 1π-serie...
Many series for 1/π were discovered since the appearance of S. Ramanujan’s famous paper “Modular equ...
We compute Ramanujan–Sato series systematically in terms of Thompson series and their modular equati...
AbstractUsing certain representations for Eisenstein series, we derive several of Ramanujan's series...
In this paper, we use the explicit Shimura Reciprocity Law to compute the cubic singular moduli α∗n,...
In 1914 S. Ramanujan recorded a list of 17 series for 1/π. We survey the methods of proofs of Ramanu...
ABSTRACT Srinivasa Ramanujan had established several hypergeometric series for the number 1/π out of...
96 pages including large numerical tables and PARI programsSome PARI programs have bring out a prope...
AbstractIn this paper our attempt is to investigate the class number problem of imaginary quadratic ...
We outline an elementary method for proving numerical hypergeometric identities, in particular, Rama...
The class number problem is one of the central open problems of algebraic number theory. It has long...
We resolve a family of recently observed identities involving 1/π using the theory of modular forms ...
AbstractIn this paper, we give parametric families of both real and complex quadratic number fields ...
Improving a result of Montgomery and Weinberger, we establish the existence of infinitely many real ...