On a generalized identity connecting theta series associated with discriminants $\varDelta $ and $\varDelta p^2$
Acta Arithmetica, Tome 176 (2016) no. 4, pp. 343-364
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
When the discriminants $\varDelta $ and $\varDelta p^2$ have one form per genus, Patane (2015) proves a theorem which connects the theta series associated to binary quadratic forms of each discriminant. This paper generalizes the main theorem of Patane (2015) by allowing $\varDelta $ and $\varDelta p^2$ to have multiple forms per genus. In particular, we state and prove an identity which connects the theta series associated to a single binary quadratic form of discriminant $\varDelta $ to a theta series associated to a subset of binary quadratic forms of discriminant $\varDelta p^2$. Here and everywhere $p$ is a prime.
Keywords:
discriminants vardelta vardelta have form per genus patane proves theorem which connects theta series associated binary quadratic forms each discriminant paper generalizes main theorem patane allowing vardelta vardelta have multiple forms per genus particular state prove identity which connects theta series associated single binary quadratic form discriminant vardelta theta series associated subset binary quadratic forms discriminant vardelta here everywhere prime
Affiliations des auteurs :
Frank Patane 1
@article{10_4064_aa8383_6_2016,
author = {Frank Patane},
title = {On a generalized identity connecting theta series associated with discriminants $\varDelta $ and $\varDelta p^2$},
journal = {Acta Arithmetica},
pages = {343--364},
publisher = {mathdoc},
volume = {176},
number = {4},
year = {2016},
doi = {10.4064/aa8383-6-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8383-6-2016/}
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Frank Patane. On a generalized identity connecting theta series associated with discriminants $\varDelta $ and $\varDelta p^2$. Acta Arithmetica, Tome 176 (2016) no. 4, pp. 343-364. doi: 10.4064/aa8383-6-2016
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