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Millions, billions & trillions : understanding big numbers
Huge numbers are hard to comprehend. This book explains quantities in terms children can understand. For example, one million dollars could buy two full pizzas a day for more than sixty-eight years.
Book
Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation
There are two main interrelated goals of this paper. Firstly we investigate the sums
eBook
A place for Zero : a math adventure
As Zero searches to find his place, he learns of his additive and multiplicative identities, and then he establishes place value.
Book
Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume
We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We
then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of
eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume
and the dynamics of their geodesic flows.
eBook
A brief history of numbers
The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century.
Book
Hypergeometric functions over finite fields
Building on the developments of many people including Evans, Greene, Katz, McCarthy, Ono, Roberts, and Rodriguez-Villegas, we
consider period functions for hypergeometric type algebraic varieties over finite fields and consequently study hypergeometric functions
over finite fields in a manner that is parallel to that of the classical hypergeometric functions. Using a comparison between the
classical gamma function and its finite field analogue the Gauss sum, we give a systematic way to obtain certain types of hypergeometric
transformation and evaluation formulas over finite fields and interpret them geometrically using a Galois representation perspective. As
an application, we obtain a few finite field analogues of algebraic hypergeometric identities, quadratic and higher transformation
formulas, and evaluation formulas. We further apply these finite field formulas to compute the number of rational points of certain
hypergeometric varieties.
eBook
100 ways to celebrate 100 days
\"It's the 100th day of school--what can you do to celebrate? Here are 100 different ideas for celebrating this fun and important day. The 100th day is about math--and so much more! From collecting to counting, baking to bouncing, reading to writing, every possible kind of activity is included for 100th day celebrations at home or at school.\"--Publisher provided.
Book
Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $\\mathbb F_p(t)$, when $p$ is prime and $r\\ge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $\\mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $\\mathbb F_q(t^1/d)$.
eBook