New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function
نویسندگان
چکیده
منابع مشابه
Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions, and Schur Functions
In this paper we derive many infinite families of explicit exact formulas involving either squares or triangular numbers, two of which generalize Jacobi’s 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. In fact, we similarly generalize to infinite families all of Jacobi’s explicitly stated degree 2, 4, 6, 8 Lambert series expansions of classical t...
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The following is the extended version of my notes from my ATC talk given on June 4, 2014 at UCLA. I begin with a basic introduction to sums-of-squares formulas, and move on to giving motivation for studying these formulas and discussing some results about them over the reals. More recent techniques have made it possible to obtain similar results over arbitrary fields, and some of these are disc...
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This paper uses a relative of BP -cohomology to prove a theorem in characteristic p algebra. Speci cally, we obtain some new necessary conditions for the existence of sums-of-squares formulas over elds of characteristic p > 2. These conditions were previously known in characteristic zero by results of Davis. Our proof uses a generalized etale cohomology theory called etale BP2.
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Landen transformation formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by changing integration variables in elliptic integrals. We rediscover known results as well as obtain more generalized Landen formulas from a very different perspective, by making use of the recently obtained periodic solutions of physically ...
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In previous work, we introduced harmonic Maass-Jacobi forms. The space of such forms includes the classical Jacobi forms and certain Maass-Jacobi-Poincaré series, as well as Zwegers’ real-analytic Jacobi forms, which play an important role in the study of mock theta functions and related objects. Harmonic Maass-Jacobi forms decompose naturally into holomorphic and non-holomorphic parts. In this...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1996
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.93.26.15004