Bulletin of the Korean Mathematical Society (대한수학회보)

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REPRESENTATIONS BY QUATERNARY QUADRATIC FORMS WITH COEFFICIENTS 1, 2, 11 AND 22

  • Bulent, Kokluce (The Institute for Computational and Experimental Research in Mathematics Brown University)
  • Received : 2022.01.27
  • Accepted : 2022.09.21
  • Published : 2023.01.31
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Abstract

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.

Keywords

Acknowledgement

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.

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