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On the additive energy of the Heilbronn subgroup
Mathematical notes. 2017. Vol. 101. No. 1. P. 58–70.
A new upper bound for the additive energy of the Heilbronn subgroup is found. Several applications to the distribution of Fermat quotients are obtained.
E. M. Novikova, Mathematical notes 2025 Vol. 118 No. 4 P. 794–810
For each integer nonnegative n, in some Hilbert space, we introduce an integral
transform H_n. It is similar to the well-known Hankel (Fourier–Bessel) transform of nth order due
to the fact that it is related to the Fourier transform and its integral kernel is expressed in terms of
the Bessel function J_n. But, unlike the Hankel transform, intended ...
Added: November 25, 2025
Lotonina K., Fedorenko Sergei Valentinovich, Olshevskaia O., , in: 2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy), 5-7 Nov. 2025.: IEEE, 2025. P. 1–4.
A novel method of construction of the discrete Fourier transform (DFT) over the finite field has been proposed. The method is based on a polynomial representation of the DFT computation. We choose to minimize the sum of the number of operations (multiplications and additions) over a finite field as the optimization criterion. The presented method ...
Added: November 10, 2025
Seidov S., Journal of Physics A: Mathematical and Theoretical 2023 Vol. 56 No. 32
Added: September 17, 2023
D. V. Gribanov, Shumilov I. A., D. S. Malyshev, Optimization Letters 2024 Vol. 18 P. 73–103
In this work we consider the problem of computing the (min,+)-convolution of two sequences a and b of lengths n and m, respectively, where n≥m. We assume that a is arbitrary, but b_i=f(i), where f(x):[0,m)→R is a function with one of the following properties: f is linear, f is monotone, f is convex, f is concave, f is piece-wise linear, f is a polynomial function of a fixed degree. To the best of our knowledge, the concave, piece-wise linear and polynomial ...
Added: May 28, 2023
Попов И. Ю., Stukach O., Зорин П. А., Динамика систем, механизмов и машин 2021 Т. 9 № 3 С. 117–121
На реальных данных коммерческого учёта тепловой энергии в многоэтажных жилых
зданиях города Томска проведены гистограммные оценки метрики общей вариации выбросов методом
полной вариации распознавания ошибок. Для сравнения выбраны данные по домам с одинаковыми и
разными схемами теплопотребления и материалом стен. Результаты моделирования показывают сложность в интерпретации получившихся зависимостей для применяемого метода и необходимость уточнения его ограничений. Подтверждена большая ...
Added: November 27, 2022
Sergei Valentinovich Fedorenko, IEEE Access 2021 Vol. 9 P. 38673–38686
A novel method for finding roots of polynomials over finite fields has been proposed.
This method is based on the cyclotomic discrete Fourier transform algorithm.
The improvement is achieved by using the normalized cyclic convolutions,
which have a small complexity and allow matrix decomposition,
as well as methods of adapting the truncated normalized cyclic convolutions calculation.
For small values of ...
Added: April 15, 2021
Fedorenko Sergei Valentinovich, IEEE Transactions on Signal Processing 2020 Vol. 68 P. 4813–4823
The new method for the discrete Fourier transform computation over a finite field is introduced.
This method is a nontrivial generalization of the Duhamel-Hollmann algorithm with replacement
of the Toeplitz convolution calculation by the normalized cyclic convolution calculation.
Both algorithms have the smallest multiplicative complexity. ...
Added: September 12, 2020
Sergei Valentinovich Fedorenko, IEEE Transactions on Signal Processing 2015 Vol. 63 No. 20 P. 5307–5317
A normalized cyclic convolution is a cyclic convolution when one of its factors is a fixed polynomial. Herein, a novel method for constructing a normalized cyclic convolution over a finite field is introduced. This novel method is the first constructive and best known method for even lengths. This method can be applied for computing discrete ...
Added: February 3, 2018
Vyugin I. V., Solodkova E. V., Shkredov I. D., Mathematical notes 2016 Vol. 100 No. 1 P. 189–198
Using Stepanov’s method, we obtain an upper bound for the cardinality of the intersection of additive shifts of several multiplicative subgroups of a finite field. The resulting inequality is applied to a question dealing with the additive decomposability of subgroups. ...
Added: October 12, 2016
Finkelberg M. V., Braverman A., Advances in Mathematics 2012 No. 230 P. 414–432
This is the second paper of the series, started by Braverman-Finkelberg (2010) which describes a conjectural analogue of the affine Grassmannian for affine Kac-Moody groups (also known as double affine Grassmannian). The current paper is dedicated to describing a conjectural analogue of the convolution diagram for the double affine Grassmannian. In case our group is ...
Added: December 3, 2012