Friable values of Piatetski-Shapiro sequences

Generalized Rudin – Shapiro sequences

Rank-One Residues of Eisenstein Series∗ Dedicated to Ilya Piatetski-Shapiro with admiration and affection

The trace-class problem was for some years a rather embarrassing unsolved problem in the theory of automorphic forms. Although the absence of a solution did not seriously obstruct progress, it did undesirably, and in the general view unnecessarily, complicate the statements of various results, especially in the context of the trace formula. Fortunately, it has recently been solved by W. Müller ...

Golay-Davis-Jedwab Complementary Sequences and Rudin-Shapiro Constructions

A Golay Complementary Sequence (CS) has a Peak-to-AveragePower-Ratio (PAPR) ≤ 2.0 for its one-dimensional continuous Discrete Fourier Transform (DFT) spectrum. Davis and Jedwab showed that all known length 2 CS, (GDJ CS), originate from certain quadratic cosets of Reed-Muller (1,m). These can be generated using the RudinShapiro construction. This paper shows that GDJ CS have a PAPR ≤ 2.0 under ...

Bounds for the discrete correlation of infinite sequences on k symbols and generalized Rudin-Shapiro sequences

Pseudorandom sequences, i.e. deterministic sequences on finite alphabets with properties reminiscent of random sequences, are an intensively studied subject. We refer to the series of papers by Mauduit and Sárközy (partly with coauthors) [2, 8, 9] among many others. A great part of the mentioned work deals with correlation measures for binary sequences. Let x = x0x1 . . . xn be a finite word ov...

Peak Side Lobe Levels of Legendre and Rudin-Shapiro Sequences: Families of Binary Sequences

Student, Assistant Professor Associate Professor Lendi Institute of Engineering and Technology, VZM, INDIA. Abstract: The peak side lobe level (PSL) is numerically estimated for Rudin-shapiro sequences and Legendre sequences which belong to the families of Binary sequences. Notable similarities are presented between PSL and merit factor behavior under cyclic rotations of the sequences (i.e. 1/4...