Add to ORKGIn this thesis, we study the problem of representing integers by quadratic forms. The formulas for the number of representations are obtained as a sum of an Eisenstein part and a cusp part. We begin by solving the representation problem for binary quadratic forms of discriminant -D<0 where the number field Q(√−D) has class number 3. We obtain formulas for the number of representations of an integer as a sum of k triangular numbers, denoted by δk(n), for even values of k. As special cases, for k=14,16 and 18, new formulas are provided in which the cusp part is given as a linear combination of certain eta products. At the end, for even values of k, we study the first and the second moments of δk(n) and prove an analogue of the Wagon's conjec...
We investigate here the representability of integers as sums of triangular numbers, where the n-th t...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
In this paper we give a formula for the number of representations of some square-free integers by ce...
The representation of integers in binary quadratic forms has been a penchant for mathematicians thro...
Abstract. We prove an explicit formula for the number of representations of an integer as the sum of...
In this paper, we present eighteen interesting infinite products and their Lambert series expansions...
Let N denote the set of positive integers and Z the set of all integers. Let N0 = N ∪ {0}. Let a1x2 ...
This paper deals with the representation by the quadratic form in three variables with odd prime inv...
The thesis discusses classical number theory problems on representations of integers by sums of two,...
In this paper, we present an analysis of some cases where a positive integer cannot berepresented by...
In this paper, we present an analysis of some cases where a positive integer cannot be represented b...
WOS: 000395321000011Using modular forms, we determine formulas for the number of representations of ...
By considering the norm of elements in the ring of integers in $\mathbb{Q}(\sqrt{-a})$, we give an a...
In this study, we calculated all reduced primitive binary quadratic forms which are . We find the th...
Abstract. Formulas are obtained for the number of representations of pos-itive integers by quadratic...
We investigate here the representability of integers as sums of triangular numbers, where the n-th t...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
In this paper we give a formula for the number of representations of some square-free integers by ce...
The representation of integers in binary quadratic forms has been a penchant for mathematicians thro...
Abstract. We prove an explicit formula for the number of representations of an integer as the sum of...
In this paper, we present eighteen interesting infinite products and their Lambert series expansions...
Let N denote the set of positive integers and Z the set of all integers. Let N0 = N ∪ {0}. Let a1x2 ...
This paper deals with the representation by the quadratic form in three variables with odd prime inv...
The thesis discusses classical number theory problems on representations of integers by sums of two,...
In this paper, we present an analysis of some cases where a positive integer cannot berepresented by...
In this paper, we present an analysis of some cases where a positive integer cannot be represented b...
WOS: 000395321000011Using modular forms, we determine formulas for the number of representations of ...
By considering the norm of elements in the ring of integers in $\mathbb{Q}(\sqrt{-a})$, we give an a...
In this study, we calculated all reduced primitive binary quadratic forms which are . We find the th...
Abstract. Formulas are obtained for the number of representations of pos-itive integers by quadratic...
We investigate here the representability of integers as sums of triangular numbers, where the n-th t...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
In this paper we give a formula for the number of representations of some square-free integers by ce...