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A Course in Arithmetic
TLDR
In this article, the theorem on arithmetic progressions modular forms is proved for finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratics forms with discriminant +-1.Abstract:
Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on arithmetic progressions modular forms.read more
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Pokroky matematiky, fyziky a astronomie
TL;DR: Volf et al. as mentioned in this paper presented the results, achieved by representatives of the Czech Republic, of the 21st century European Union Science Olympiad (EUSO), which has not even reached ten years.
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Quadratic Forms Representing All Odd Positive Integers
TL;DR: In this paper, the authors considered the problem of classifying all positive-definiteinteger-valued quaternary quadratic forms that represent all positive odd integers, and they gave a list of 23 candidates and showed that 19 of them represent positive odds.
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Fermionic rational conformal field theories and modular linear differential equations
TL;DR: In this paper, the authors define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups of the fermionic Rational Conformal Field Theories (RCFTs).
The Atiyah-Singer index theorem
Nigel Higson,John Roe +1 more
TL;DR: The Atiyah-Singer Index Theorem as mentioned in this paper provides a topological formula, in terms of characteristic classes, of the Fredholm index of certain elliptic operators, and had influenced, since its discovery in the 1960s, many areas of mathematics.
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Weak approximation on del Pezzo surfaces of degree 1
TL;DR: In this article, the authors study del Pezzo surfaces of degree 1 of the form w^2 = z^3 + Ax^6 + By^6 in the weighted projective space P_k(1,1,2,3), where k is a perfect field of characteristic not 2 or 3 and A,B \in k^*.