Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramanujan's Identities and Representation of Integers by Certain Binary
  and Quaternary Quadratic Forms   We revisit old conjectures of Fermat and Euler regarding representation of
integers by binary quadratic form x^2+5y^2. Making use of Ramanujan's_1\psi_1
summation formula we establish a new Lambert series identity for
\sum_{n,m=-\infty}^{\infty} q^{n^2+5m^2}. Conjectures of Fermat and Euler are
shown to follow easily from this new formula. But we don't stop there.
Employing various formulas found in Ramanujan's notebooks and using a bit of
ingenuity we obtaina collection of new Lambert series for certain infinite
products associated with quadratic forms such as x^2+6y^2, 2x^2+3y^2,
x^2+15y^2, 3x^2+5y^2, x^2+27y^2, x^2+5(y^2+ z^2+ w^2), 5x^2+y^2+ z^2+ w^2. In
the process, we find many new multiplicative eta-quotients and determine their
coefficients.

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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph