Representations by quaternary quadratic forms with coefficients 1, 2, 11 and 22

Bulent Kokluce

doi:10.4134/BKMS.b220078

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Journal article

Representations by quaternary quadratic forms with coefficients 1, 2, 11 and 22

Bulent Kokluce

Bulletin of the Korean Mathematical Society, Vol.60(1), pp.237-255

2023

DOI: https://doi.org/10.4134/BKMS.b220078

Abstract

modular forms

cusp forms

theta products

quadratic forms

Eisenstein series

representation numbers

Eta quotients

Dedekind eta function

In this article, we find bases for the spaces of modular forms $M_2({\Gamma}_0(88),\;({\frac{d}{\cdot}}))$ for d = 1, 8, 44 and 88. We then derive formulas for the number of representations of a positive integer by the diagonal quaternary quadratic forms with coefficients 1, 2, 11 and 22.

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Title: Representations by quaternary quadratic forms with coefficients 1, 2, 11 and 22
Creators: Bulent Kokluce - Department of Mathematics
Publication Details: Bulletin of the Korean Mathematical Society, Vol.60(1), pp.237-255
Publisher: KOREAN MATHEMATICAL SOC
Number of pages: 19
Grant note: Simons Foundation Institute: 507536
The author thanks the anonymous referee for reading the manuscript carefully and the editor and Fabien Clery for the helpful comments. This material is based upon a work supported by the Simons Foundation Institute Grant Award ID 507536 while the author was in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI.
Academic Unit: Department of Mathematics
Resource Type: Journal article
DOI: https://doi.org/10.4134/BKMS.b220078
Record Identifier: 9914500264001301

Representations by quaternary quadratic forms with coefficients 1, 2, 11 and 22

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