Binary quadratic forms and the Fourier coefficients of certain weight 1 \(\eta\)-quotients

DOI10.1016/j.jnt.2013.08.016zbMath1385.11009arXiv1302.2359OpenAlexW2012667892MaRDI QIDQ2406713

Frank Patane, Alexander Berkovich

Publication date: 5 October 2017

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.2359

zbMATH Keywords

binary quadratic formstheta seriesmultiplicative functionsHecke operatorseta-quotientsdissections of \(q\)-series

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Theta functions and abelian varieties (14K25) Theta series; Weil representation; theta correspondences (11F27) General binary quadratic forms (11E16)

Related Items (6)

The number of partitions with distinct even parts revisited ⋮ Some expressions for binary theta series by eta-quotients and their applications ⋮ On the Gauss \(E\Upsilon PHKA\) theorem and some allied inequalities ⋮ Eta quotients of level 12 and weight 1 ⋮ A proof of Hecke’s formula for binary quadratic forms ⋮ An identity connecting theta series associated with binary quadratic forms of discriminant \(\Delta\) and \(\Delta(\mathrm{prime})^2\)

Cites Work

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• Quadratic forms that represent almost the same primes
• The expansion of ∏_k=1^∞(1-q^ak)(1-q^bk)
• ON η3( aτ) η3( bτ) WITH a+ b=8
• EXPLICIT FORMULAS FOR THE FOURIER COEFFICIENTS OF A CLASS OF ETA QUOTIENTS
• On Rogers–Ramanujan functions, binary quadratic forms and eta-quotients
• On the number of representations of n by ax²+bxy+cy²

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