On the Number of Representations of a Natural Number by Certain Quaternary Quadratic Forms
In this paper, we find a basis for the space of modular forms of weight 2 on \(\Gamma _1(48)\) and then use this basis to find formulas for the number of representations of a positive integer n by certain quaternary quadratic forms which are of the form \
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B. Ramakrishnan Bernhard Heim Brundaban Sahu Editors
Modular Forms and Related Topics in Number Theory Kozhikode, India, December 10–14, 2018
Springer Proceedings in Mathematics & Statistics Volume 340
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B. Ramakrishnan Bernhard Heim Brundaban Sahu •
•
Editors
Modular Forms and Related Topics in Number Theory Kozhikode, India, December 10–14, 2018
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Editors B. Ramakrishnan Statistics and Applied Mathematics CUTN Thiruvarur, India
Bernhard Heim Faculty of Mathematics, Computer Science, and Natural Sciences RWTH Aachen University Aachen, Germany
Brundaban Sahu School of Mathematical Sciences NISER Bhubaneswar, Odisha, India
ISSN 2194-1009 ISSN 2194-1017 (electronic) Springer Proceedings in Mathematics & Statistics ISBN 978-981-15-8718-4 ISBN 978-981-15-8719-1 (eBook) https://doi.org/10.1007/978-981-15-8719-1 Mathematics Subject Classification: 11-XX, 11Fxx, 11F37, 11F41 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registe
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