409 citations
- City University of New YorkUS138 papers
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4 papers · 2 filters
Generalization of Ramanujan's formula for sums of half-integer powers of consecutive integers via formal Bernoulli series
Max A. Alekseyev, Rafael Gonzalez, Keryn Loor +2
Faulhaber's formula expresses the sum of the first positive integers, each raised to an integer power , as a polynomial in of degree . Ramanujan expressed thi…
Compression and complexity for sumset sizes in additive number theory
Melvyn B. Nathanson
The study of sums of finite sets of integers has mostly concentrated on sets with small sumsets (Freiman's theorem and related work) and on sets with large sumsets (Sidon sets and…
Explicit sumset sizes in additive number theory
Melvyn B. Nathanson
It is an open problem in additive number theory to compute and understand the full range of sumset sizes of finite sets of integers, that is, the set $\mathcal{R}_{\mathbf{Z}}(h,k)…
-independence and the construction of -sets of integers and lattice points
Melvyn B. Nathanson
This paper gives a simple -vector space construction of finite -sets of integers and lattice points.