Lower bounds for sums of powers of different natural numbers expressed as functions of the sum of these numbers.
Lower bounds for the conductor of L-functions
Lower bounds for the discrepancy of some sequences
Lower Bounds for the Discrepancy of Triples of Inversive Congruential Pseudorandom Numbers with Power of Two Modulus.
Lower bounds for the greatest prime factor of
Lower bounds for the largest eigenvalue of the gcd matrix on
Consider the matrix with ’th entry . Its largest eigenvalue and sum of entries satisfy . Because cannot be expressed algebraically as a function of , we underestimate it in several ways. In examples, we compare the bounds so obtained with one another and with a bound from S. Hong, R. Loewy (2004). We also conjecture that for all . If is large enough, this follows from F. Balatoni (1969).
Lower bounds for the largest prime factor of an odd perfect number which is divisible by a Fermat prime.
Lower bounds for the number of integral polynomials with given order of discriminants
Lower bounds for the principal genus of definite binary quadratic forms.
Lower bounds for the solutions in the second case of Fermat's equation with prime power exponents
Lower bounds of discrete moments of the derivatives of the Riemann zeta-function on the critical line
We establish unconditional lower bounds for certain discrete moments of the Riemann zeta-function and its derivatives on the critical line. We use these discrete moments to give unconditional lower bounds for the continuous moments , where is a non-negative integer and a rational number. In particular, these lower bounds are of the expected order of magnitude for .
Lower bounds of heights of points on hypersurfaces
Lower bounds on the projective heights of algebraic points
Lower limit for the number of sets of solutions of xe + ye + ze ... 0 (mod p).
Lower order terms for the one-level densities of symmetric power L-functions in the level aspect
Lower order terms in the 1-level density for families of holomorphic cuspidal newforms
Lower order terms of the second moment of S(t)
Lower powers of elliptic units
In the previous paper [Sch2] it has been shown that ray class fields over quadratic imaginary number fields can be generated by simple products of singular values of the Klein form defined below. In the present article the second named author has constructed more general products that are contained in ray class fields thereby correcting Theorem 2 of [Sch2]. An algorithm for the computation of the algebraic equations of the numbers in Theorem 1 of this paper has been implemented in a KASH program...
Lp-bounds for spherical maximal operators on Zn.
We prove analogue statements of the spherical maximal theorem of E. M. Stein, for the lattice points Zn. We decompose the discrete spherical measures as an integral of Gaussian kernels st,ε(x) = e2πi|x|2(t + iε). By using Minkowski's integral inequality it is enough to prove Lp-bounds for the corresponding convolution operators. The proof is then based on L2-estimates by analysing the Fourier transforms ^st,ε(ξ), which can be handled by making use of the circle method for exponential sums. As a...
Lₚ-deviations from zero of polynomials with integral coefficients