A simple, elementary method is given for deriving estimates of sums of arithmetic functions, the estimates being in a certain sense uniform over a class of functions appearing in the summation. The ...

https://doi.org/10.4169/college.math.j.43.4.321 • https://www.jstor.org/stable/10.4169/college.math.j.43.4.321 Copy URL ...

Bilinear forms and character sums have emerged as pivotal tools in analytic number theory, offering robust frameworks for investigating sums wherein variables interact multiplicatively. Bilinear forms ...

Consider this sequence of numbers: 5, 7, 9. Can you spot the pattern? Here’s another with the same pattern: 15, 19, 23. One more: 232, 235, 238. “Three equally spaced things,” says Raghu Meka, a ...

The simple definition of a mean is that of a numeric quantity which represents the center of a collection of numbers. Here the trick lies in defining the exact type of numeric collection, as beyond ...

Before the 13th century Europeans used Roman numerals to do arithmetic. Leonardo of Pisa, better known today as Fibonacci, is largely responsible for the adoption of the Hindu–Arabic numeral system in ...

A long-standing puzzle seems to constrain how addition and multiplication relate to each other. A graduate student has gone further than anyone else in establishing the connection. In 1983 the ...

Randolph Grace receives funding from the Marsden Fund, administered by the Royal Society of New Zealand. University of Canterbury provides funding as a member of The Conversation AU. University of ...

You may never have heard of modular arithmetic, but you use it every day without the slightest difficulty. In this system, numbers wrap around when they reach a certain size called the modulus; it is ...