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"This book offers something new, every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes, (i) the correspondence between the forms of half-integral weight and those of integral weight and (ii) the arithmeticity of various Dirichlet series associated with modular forms of integral or half-integral weight."

"In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces."

"Partitions, q-series, and modular forms contains a collection of research and survey papers that grew out of a Conference on partitions, q-series and modular forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions."

"ABSTRAKTujuan utama dari keamanan komunikasi adalah mencegah data pesan dari akses pihak ketiga. Solusi dari masalah tersebut adalah menerapkan enkripsi End-to-end. Algoritma enkripsi Elliptic Curve Cryptography (ECC) cocok digunakan sebagai metode enkripsi End-to-end pada sistem komunikasi digital termasuk aplikasi chat. ECC adalah jenis kriptografi kunci publik yang mendasarkan keamanannya pada permasalahan matematis dari kurva eliptik, ECC mempunyai tingkat keamanan yang setara dengan RSA menggunakan kunci berukuran lebih kecil. Penelitian ini membahas perancangan dan implementasi dari algoritma enkripsi dan dekripsi yang menerapkan kriptografi ECC sebagai metode enkripsi End-to-end pada aplikasi chat. Algoritma ini menggunakan operasi matematika dan nilai parameter dari kurva eliptik untuk menghasilkan kunci serta ciphertextnya dan juga melakukan dekripsi. Dari hasil ujicoba dan analisa implementasi enkripsi dan dekripsi menggunakan algoritma ECC, algoritma tersebut cocok digunakan sebagai metode enkripsi End-to-end, karena ukuran kunci yang relatif ringan dan operasi matematika yang menggunakan parameter khusus yang berbeda-beda. Hasil pengujian enkripsi dan dekripsi menggunakan parameter kurva eliptik secp192r1 dan secp192k1 yang mempunyai ukuran kunci sekitar 2¹⁹² bit, menghasilkan kunci dan ciphertext paling ringan dan paling cepat diproses, dengan angka nilai keduanya berukuran sepanjang 58 digit.

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ABSTRACTThe main purpose of communication security is to prevent message data from third party access. The solution to this problem is to implement End-to-end encryption. Elliptic Curve Cryptography (ECC) encryption algorithm is suitable for use as an End-to-end encryption method on digital communication systems including chat applications. ECC is a type of public key cryptography that bases its security on mathematical problems from elliptic curves, ECC has a level of security equals to RSA while using smaller keys. This study discusses the design and implementation of encryption and decryption algorithms that apply ECC cryptography as an End-to-end encryption method in chat applications. This algorithm uses mathematical operations and parameter values from the elliptic curve to generate keys and their ciphertext and also decrypt them. From the results of testing and analyzing the implementation of encryption and decryption using the ECC algorithm, the algorithm is suitable for use as an End-to-end encryption method, because of the relatively light key size and mathematical operations that use different parameters. The results of encryption and decryption testing using elliptic curve parameters secp192r1 and secp192k1 which have a key size of about 2¹⁹² bits, produce the lightest and fastest to process ciphertext and keys, with the value of both measuring 58 digits.

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