representationstheta functionsDedekind eta functioneta quotientsEisenstein seriesEisenstein formsmodular formscusp formsUsing modular forms, we determine formulas for the number of representations of a positive integer by diagonal octonary quadratic forms with coefficients 1, 2, 3 or 6....
A very useful fact in additive combinatorics is that analytic expressions that can be used to count the number of structures of various kinds in subsets of Abelian groups are robust under quasirandom perturbations, and moreover that quasirandomness can o
S. M. Voronin, “On the zeros of zeta-functions of quadratic forms,” in Trudy Mat. Inst. Steklov Vol. 142: Number Theory, Mathematical Analysis, and Their Applications, Collected papers in honor of the eighty-fifth birthday of Academician I. M. Vinogradov (Nauka, Moscow, 1976), pp. 13...
Each of these problems is a fractional programming problem involving the maximization of a ratio of a convex function to a convex function, where at least one of the convex functions is a quadratic form. First, the article presents and validates a number of theoretical properties of these ...
Quadratic formssum of divisors functionsconvolution sumsrepresentation numbersLet N(a1, u2026, a4; n) denote the number of representations of an integer n by the form $a_{1}(x_{1}^{2}+x_{1}x_{2}+x_{2}^{2})+a_{2}(x_{3}^{2}+x_{3}x_{4}+x_{4}^{2})+a_{3}(x_...
Distributions of Quadratic FormsRANDOM VARIABLESDISTRIBUTION FUNCTIONSCHI SQUARE TESTAPPROXIMATION(MATHEMATICSSERIES(MATHEMATICSINFINITE SERIESBESSEL FUNCTIONSDEGREES OF FREEDOMACCURACYALGORITHMSsummaryExact expressions for the distribution function of a random variable of the form c1χ2m+c2χ2n are given where ...
from elementary and combinatorial (a modern example being escalations used in the proof of 290-Theorem), through algebraic (such as the classical connection to class groups of real quadratic number fields or local-global principles) to analytic (theta functions, circle method, or Siegel’s mass ...
英文: With the theory of quadratic form, this essay gives out another way to solve the extremum problems of multi-variable functions.中文: 摘要文章以二次型理论为依据,提出了解决多元函数极值问题的另一种方法。英文: Quadratic Tensive Spline Function中文: 二次张力样条函数 ...
Coprime-universal quadratic forms 57:06 Correlations of multiplicative functions along beatty sequence 36:18 counting sign changes 54:04 cubic weyl sums with smooth denominator 01:03:57 Delta method and its application to the Rankin-selberg problem 51:33 Detecting primes in multiplicatively ...
G. A. Lomadze, “Formulas for the number of representations of numbers by certain regular and semiregular ternary quadratic forms, belonging to two-class genera,”34, No. 2, 131–162 (1978). Yu. I. Manin, “Nonarchimedean integration and p-adic L-functions of Jacquet-Langlands,” Usp....