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"NUMERALS"
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Fun with Roman numerals
Explains the Roman numeral system, which, though very old, is still in use today.
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
City by numbers
Paintings of various sites around New York City-- from a shadow on a building to a wrought iron-gate to the Brooklyn Bridge-- depict the numbers from one to twenty-one.
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
L'incroyable histoire du chiffre 3
\"C'est une belle soirée sous la tente. Le public est en délire et le maître de cérémonie s'apprête à commencer le spectacle tant attendu: l'histoire de l'incroyable, du mirobolant, de l'époustouflant chiffre 3! Mais le pauvre n'arrive pas à faire son numéro, car il ne cesse d'être interrompu par deux personnages...agaçants: Souris qui remet TOUT en question et Singe à l'imagination TRÈS fertile. Pourquoi est-ce que le chiffre 3 recevrait TOUTE l'attention? C'est INJUSTE! Singe et Souris prennent donc le contrôle du spectacle. Ils amèneront les lecteurs.rices et le pauvre maître de cérémonie à les suivre dans les méandres d'une histoire peu conventionnelle.\"--leslibraires.ca.
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